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The article presents comments on the management science paper "On Sequencing n Jobs on One Machine to Minimize the Number of Late Jobs," by William L. Maxwell. The paper focused on an integer programming formulation of a one-machine job shop problem. The author contends that Maxwell made in error in proving the validity of an optimal algorithm by applying cutting plane constraints to the problem. The author explains that the problem cannot be solved through traditional cutting plane procedures. The author provides a mathematical model in an attempt to correct the proof.

This paper studies the convergence properties of the well-known message-passing algorithm for convex optimisation. Under the assumption of pairwise separability and scaled diagonal dominance, asymptotic convergence is established and a simple bound for the convergence rate is provided for message-passing. In comparison with previous results, our results do not require the given convex program to have known convex pairwise components and that our bound for the convergence rate is tighter and simpler. When specialised to quadratic optimisation, we generalise known results by providing a very simple bound for the convergence rate. [ABSTRACT FROM AUTHOR]

Generating units, participating in the secondary frequency control of a control area, are usually spinning units already connected to the network and operating outside their range of optimal performance. This paper deals with an alternative method of providing secondary frequency control called Rapid-Start (RS). It consists in assigning a regulation band to several off-line units (RS units) which are capable of being started and connected rapidly, therefore allowing the online units to operate closer to their nominal power. As RS operation may have economic benefits, an appropriate algorithm to start up an RS unit needs to be developed. This paper proposes a methodology to evaluate, compare, and choose the most appropriate RS algorithm among the ones developed for a certain AGC control area. An optimization model provides a reference by determining the hypothetically ideal start-ups and shut-downs of RS units. In addition, the definition of performance indexes to evaluate, compare, and choose the different RS algorithms is proposed. The proposed methodology is illustrated for a secondary frequency control zone within the Spanish power system by using real data signals. [ABSTRACT FROM PUBLISHER]

Estimating the probability of failures or accidents with aerospace systems is often necessary when new concepts or designs are introduced, as it is being done for autonomous aircraft. If the design is safe, as it is supposed to be, accident cases are hard to find. Such analysis needs some variance reduction technique and several algorithms exist for that; however, specific model features may cause difficulties in practice, such as the case of system models where independent agents have to autonomously accomplish missions within finite time, and likely with the presence of human agents. For handling these scenarios, this paper presents a novel estimation approach, based on the combination of the well-established variation reduction technique of interacting particles system with the long-standing optimization algorithm denominated DIviding RECTangles. When combined, these two techniques yield statistically significant results for extremely low probabilities. In addition, this novel approach allows the identification of intermediate events and simplifies the evaluation of sensitivity of the estimated probabilities to certain system parameters. [ABSTRACT FROM AUTHOR]

Timing performance and routability are two main goals of global muting. These two targets are mutually conflicting if we view and handle their effects independently. In this paper, we adopt a shadow price mechanism to incorporate the two issues into one unified objective function. We formulate global routing as a multicommodity flow problem. The objective function is the slack of congestion with the clock period as the delay limit from registers and inputs to registers and outputs. The multicommodity flow is expressed by a linear-programming formulation as a primal problem. We then convert the primal problem Into a dual formulation using the shadow price as the variables. The shadow price of a net is the sum of its congestion price and timing price. The primal and dual formulation offers theoretical upper and lower bounds of the routing solution. Throughout the optimization process, the difference of the two bounds reduces, which provides the user's insight into the quality of the solutions. Based on the new formulation, this paper presents the UTACO algorithm for standard cell global routing. [ABSTRACT FROM AUTHOR]

This paper presents a computational tool intended to calculate and minimize the electric fields at ground level of high surge impedance loading transmission lines (TLs). This type of TL achieves higher power transmission rates utilizing optimized configuration for the phase conductors. This method is advantageous over other actions taken by the utility company, such as increasing the maximum operation temperature of the line, increasing the size of the conductors, or the utilization of multiple conductors per phase. In this paper, an enhanced deep-cut ellipsoidal method is applied to find a new optimized configuration for the phase conductors. The new proposed configuration results in reduced profiles of electric fields. Two different TLs are analyzed and optimized. [ABSTRACT FROM PUBLISHER]

In this paper, we tackle the problem of multi-cell resource scheduling, where the objective is to maximize the weighted sum-rate through inter-cell interference coordination (ICIC). The blanking method is used to mitigate the inter-cell interference, where a resource is either used with a predetermined transmit power or not used at all, i.e., blanked. This problem is known to be strongly NP-hard, which means that it is not only hard to solve in polynomial time, but it is also hard to find an approximation algorithm with guaranteed optimality gap. In this work, we identify special scenarios where a polynomial-time algorithm can be constructed to solve this problem with theoretical guarantees. In particular, we define a dominant interference environment, in which for each user the received power from each interferer is significantly greater than the aggregate received power from all other weaker interferers. We show that the originally strongly NP-hard problem can be tightly relaxed to a linear programming problem in a dominant interference environment. Consequently, we propose a polynomial time distributed algorithm that is not only guaranteed to be tight in a dominant interference environment, but which also computes an upper bound on the optimality gap without additional computational complexity. The proposed scheme is based on the primal-decomposition method, where the problem is divided into a master-problem and multiple subproblems. We solve the master-problem iteratively using the projected-subgradient method. We also show that each subproblem has a special network flow structure. By exploiting this network structure, each subproblem is solved using the network-based optimization methods, which significantly reduces the complexity in comparison to the general-purpose convex or linear optimization methods. In comparison with baseline schemes, simulation results of the International Mobile Telecommunications-Advanced (IMT-Advanced) scenarios show that the proposed scheme achieves higher gains in aggregate throughput, cell-edge throughput, and outage probability. [ABSTRACT FROM PUBLISHER]

This paper is concerned with a linear fractional problem of the form: max[sub x] min[sub y] F(X, Y) = (cX + dY + α)/(fX + gY + β), subject to AX + BY less than or equal to b; X, Y greater than or equal to O. This problem represents a generalization of a problem considered in the literature in which F(X, Y) is assumed to be linear. A number of results for the linear case are extended; and, in particular, it is shown that this fractional max-min problem is equivalent to a quasi-convex programming problem whose optimal solution lies at a vertex of the feasible region. Using these results, we develop an algorithm for solving this problem. The paper concludes with a numerical example. [ABSTRACT FROM AUTHOR]

This paper considers unimodular sequence synthesis under similarity constraint for both the continuous and discrete phase cases. A computationally efficient iterative algorithm for the continuous phase case (IA-CPC) is proposed to sequentially optimize the quadratic objective function. The quadratic optimization problem is turned into multiple one-dimensional optimization problems with closed-form solutions. For the discrete phase case, we present an iterative block optimization algorithm. Specifically, we partition the design variables into $K$ blocks, and then, we sequentially optimize each block via exhaustive search while fixing the remaining $K-1$ blocks. Finally, we evaluate the computational costs and performance gains of the proposed algorithms in comparison with power method-like and semidefinite relaxation related techniques. [ABSTRACT FROM PUBLISHER]

To reduce field-programmable gate array power, Vdd programmability has been recently proposed to select the Vdd level for interconnects and power-gate unused interconnects. However, Vdd-level converters used in the existing Vdd-programmable method consume a large amount of leakage. This paper proposes two ways to avoid using level converters in interconnects, namely; 1) tree-based level converter insertion (TLC) and 2) dual-Vdd tree-based level converter insertion (dTLC). TLC enforces that there is only one Vdd level within each routing tree, while dTLC can have different Vdd levels within a routing tree, but no VddL switch drives VddH switches. Dual-Vdd assignment algorithms were developed considering chip-level time slack allocation for maximum power reduction. The algorithms include TLC-S and dTLC-S, two power sensitivity-based algorithms with implicit time slack allocation, and dTLC-LP, a linear programming (LP)-based algorithm with explicit time slack allocation. All allocate time slack first to interconnects with higher power sensitivity and assign low Vdd to them for more power reduction. Experiments show that dTLC-LP obtains the lowest power consumption. Compared to dTLC-LP, dTLC-S obtains a slightly higher power consumption but runs three times faster. Compared to the existing segment-based level converter insertion for dual Vdd, dTLC-LP reduces interconnect power by 52.90% without performance loss for Microelectronics Center of North Carolina benchmark circuits. [ABSTRACT FROM AUTHOR]

This paper is to develop first order necessary optimality conditions for a mathematical program with second-order cone complementarity constraints (MPSCC) which includes the mathematical program with (vector) complementarity constraints (MPCC) as a special case. Like the case of MPCC, Robinson's constraint qualification fails at every feasible point of MPSCC if we treat the MPSCC as an ordinary optimization problem. Using the formulas of regular and limiting coderivatives and generalized Clarke's Jacobian of the projection operator onto second-order cones from the literature, we present the S-, M-, C- and A-stationary conditions for a MPSCC problem. Moreover, several constraint qualifications including MPSCC-Abadie CQ, MPSCC-LICQ, MPSCC-MFCQ and MPSCC-GMFCQ are proposed, under which a local minimizer of MPSCC is shown to be a S-, M-, C- or A-stationary point. [ABSTRACT FROM AUTHOR]

This paper deals with systems (such as electronic devices and corporations) that are designed to accomplish multiple goals and whose internal structures are characterized by networks of interacting component parts. Each component of such a system is typically associated with a probability of failure, while each system goal is associated with a reward value. Failure of any network component may ultimately result in the inability to achieve one or more goals and force the forfeiture of the associated rewards. A basic problem in component-system design is to determine how the expectation of total reward may be maximized through the cost-limited acquisition of redundant (backup) components. This paper provides a formal statement of this redundancy-optimization problem and argues that the problem may not be solved easily by standard linear or integer programming techniques. It introduces an algorithm to solve this problem, proves its convergence, and presents computational results taken from a battery of test problems and an algorithm-efficiency study based on these tests. [ABSTRACT FROM AUTHOR]

This paper develops a new cutting plane for primal integer programming. This cut, when it exists and is used as pivot row, has the property that the minimum of the simplex evaluators of the next tableau is strictly larger (by an integer) than the minimum for the current tableau. The paper gives a sufficient condition in the form of a linear program for the existence of such a cut, and proposes an algorithm for generating such cuts. It also presents two additional sufficient conditions. The process of cut generation is then imbedded into a convergent primal algorithm to be used in an attempt to overcome the proof-of-optimality problem experienced with the primal algorithm. [ABSTRACT FROM AUTHOR]

This paper examines the problem of deriving the tangent (or market) portfolio from a given set of risky assets and a specified risk-free borrowing and lending rate. Deriving the tangent portfolio involves solving a mathematical programming problem which can be specified as the minimization of a quadratic objective function with linear constraints. The complementary pivot algorithm has previously been shown to be capable of deriving the optimal solution to certain quadratic programming problems, subject to a nonnegativity constraint. This paper demonstrates that the algorithm can be used to derive the tangent portfolio and that the nonnegativity constraint does not pose any serious handicap. Furthermore, it is shown that the algorithm can efficiently solve large-scale problems of this nature. [ABSTRACT FROM AUTHOR]

This paper, which is presented in two parts, is a contribution to the theory of fractional programming, i.e. maximization of quotients subject to constraints. In Part 1, duality theory for linear and concave-convex fractional programs is developed and related to recent results by Bector, Craven-Mond, Jagannathan, Sharma-Swarup, et al. Basic duality theorems of linear, quadratic and convex programming are extended. In Part II Dinkelbach's algorithm solving fractional programs is considered. The rate of convergence as well as a priori and a posteriori error estimates are determined. In view of these results the stopping rule of the algorithm is changed. Also the starting rule is modified using duality as introduced in Part I. Furthermore a second algorithm is proposed. In contrast to Dinkelbach's procedure the rate of convergence is still controllable. Error estimates are obtained too. [ABSTRACT FROM AUTHOR]

This paper investigates the optimal allocation of the marketing budget within the marketing-mix decision variables so that sales (or profit) is maximized in a planning horizon. Since the influence of marketing mix variables upon sales are, in reality, nonlinear and interactive, a geometric programming algorithm is used that solves this problem. A procedure to estimate a functional of sales on the marketing mix and environmental variables utilizing the experienced judgments of the firm's executives and the raw data is provided. The derived functional is later optimized by the Geometric Programming algorithm under a constraint set consisting of budget and strategy restrictions imposed by a firm's marketing environment, and conditions under which the optimal solution is either local or global are identified. An empirical application for a large midwestern brewery is provided which utilizes and illustrates both the estimation an optimization procedures. [ABSTRACT FROM AUTHOR]

This paper is concerned with the set covering problem (SCP), and in particular with the development of a new algorithm capable of solving large-scale SCPs of the size found in real-life situations. The set covering problem has a wide variety of practical applications which, in general, yield large and sparse instances, normally with hundreds of rows and thousands of columns. In this paper, we present an algorithm capable of solving problems of this size and test problems up to 400 rows and 4000 columns arc solved. The method developed in this paper consists of a tree-search procedure based on a combination of decomposition and state space relaxation which is a technique developed for obtaining lower bounds on the dynamic program associated with a combinatorial optimization problem. The large size SCPs are decomposed into many smaller SCPs which are then solved or bounded by state space relaxation (SSR). Before using the decomposition and SSR, reductions both in the number of columns and the number of rows of the problem are made by applying Lagrangian relaxation, linear programming and heuristic methods. [ABSTRACT FROM AUTHOR]

In order to obtain a good optimization method for the electrical transformer design with optimal selection of parameters, performance evaluation of three evolutionary algorithms (EAs), namely, genetic algorithm (GA), differential evolution algorithm, and nondominated sorting GA (NSGA-II), is carried out. The aim of this paper is to optimize parameters of transformer design (core thicknesses, primary-turn number, secondary-turn number, primary conductor area, and secondary conductor area) for minimization of total power losses (no-load losses and load losses) in three-phase transformer topology while maintaining high efficiency and low cost. The method used for this optimization scheme combines the finite-element method (FEM) and EAs to provide an accurate selection of parameters together with the optimized magnetic flux density and decreased loss. Experimental results show that NSGA-II+FEM model successfully provides a global feasible solution by minimizing total loss and related cost while improving the efficiency of three-phase transformer, rendering it suitable for application in the design environment of industrial transformers. [ABSTRACT FROM AUTHOR]

A complementary programming problem is a linear programming problem with the additional restriction that xpxq=0 holds for each specified pair (xp, xq). This paper obtains constraints called C-cuts from the restriction xpxq=0, and uses them to facilitate the computation of the branch-and-bound procedure proposed in an earlier paper [Opns. Res. 19, 1523–1528 (1971)]. Some computational results are also reported. [ABSTRACT FROM AUTHOR]

It is challenging to design effective scheduling algorithms for multimedia transmissions over wireless channels that employ adaptive modulation and coding (AMC). On the one hand, it is desirable for the overall system throughput to be enhanced by taking advantage of multi-user diversity. On the other hand, fairness or QoS guarantees need to be maintained for individual users, especially in the case of multimedia applications that have strict delay requirements. In this paper, we propose a novel scheduling algorithm called QoS-based cross-layer scheduling (QoS-CLS) to achieve a good design tradeoff. To maximize the system throughput, the algorithm takes into account the information on both the physical layer and the data link layer to schedule user transmissions. Using cross-layer information, the scheduling problem is formulated as a Markov Decision Process and the optimal decision policy (based on the channel status, traffic state, and buffer status of each traffic flow) is pre-calculated by linear programming. This policy is then stored in the system for scheduling in real-time. Simulation results show that QoS-CLS can greatly enhance the channel throughput compared to existing algorithms because of its cross-layer QoS consideration and the optimization method. Moreover, it can provide QoS guarantees while achieving efficient resource sharing among different traffic flows. [ABSTRACT FROM AUTHOR]

An algorithm is developed for multimodal design optimization of a V-shaped magnet interior permanent magnet synchronous machine (IPMSM). This algorithm is capable of finding all the local and global minima of a given single- or multi-objective function. The paper demonstrates the algorithm to minimize the total active weight of an IPMSM while minimizing its losses considering mechanical, thermal, and magnetic constraints. Predicted operating characteristics of a preliminary, nonoptimized IPMSM are compared with the global and local optimal solutions obtained. The proposed algorithm provides the designer with a complete view of alternative optimal machine designs from which a suitable design may be selected. The close agreement between the simulation and experimental results for the globally optimized IPMSM design verifies the accuracy of the optimization approach. [ABSTRACT FROM AUTHOR]

The problem ( LFP) of finding a feasible solution to a given linear semi-infinite system arises in different contexts. This paper provides an empirical comparative study of relaxation algorithms for ( LFP). In this study we consider, together with the classical algorithm, implemented with different values of the fixed parameter (the step size), a new relaxation algorithm with random parameter which outperforms the classical one in most test problems whatever fixed parameter is taken. This new algorithm converges geometrically to a feasible solution under mild conditions. The relaxation algorithms under comparison have been implemented using the extended cutting angle method for solving the global optimization subproblems. [ABSTRACT FROM AUTHOR]

Existing minimum-symbol-error-rate equalizers were derived based on the symbol-error-rate objective function. Due to the complexity of the objective function the derivation is not straightforward. In this paper we present a new approach to derive the minimum-symbol-error-rate adaptive equalizers. The problem is formulated as minimizing the norm between two subsequent parameter vectors under the constraint of symbol-error-rate minimization. The constrained optimization problem then is solved with the Lagrange multiplier method, which results in an adaptive algorithm with normalization. Simulation results show that the proposed algorithm outperforms the existing adaptive minimum-symbol-error-rate equalizer in convergence speed and steady-state performance. [ABSTRACT FROM AUTHOR]

The paper lists the problems hindering the use in business practices of the results of solving direct and inverse problems in linear programming. It is shown that overcoming these obstacles lies in the way of using of developed by the author and described in this paper method of structural optimization and algorithms for its implementation. Here are some examples of solutions by the method of structural optimization of production planning problems. [ABSTRACT FROM AUTHOR]

This paper studies the optimal inspection of autonomous robots in a complex pipeline system. We solve a 3-D region-guarding problem to suggest the necessary inspection spots. The proposed hierarchical integer linear programming optimization algorithm seeks the fewest spots necessary to cover the entire given 3-D region. Unlike most existing pipeline inspection systems that focus on designing mobility and control of the explore robots, this paper focuses on global planning of the thorough and automatic inspection of a complex environment. We demonstrate the efficacy of the computation framework using a simulated environment, where scanned pipelines and existing leaks, clogs, and deformation can be thoroughly detected by an autonomous prototype robot. [ABSTRACT FROM PUBLISHER]

In this paper, we present a linear programming solution for sign pattern recovery of a sparse signal, x, from noisy random projections of the signal. We consider two types of noise models: input noise, where noise enters before the random projection, and output noise, where noise enters after the random projection. Sign pattern recovery involves the estimation of sign pattern of a sparse signal. Our idea is to pretend that no noise exists and solve the noiseless \ell_1 problem, namely, \min \Vert \beta\Vert_1\ s.t.\ y=G \beta and quantizing the resulting solution. We show that the quantized solution perfectly reconstructs the sign pattern of a sufficiently sparse signal. Specifically, we show that the sign pattern of an arbitrary k-sparse, n-dimensional signal x can be recovered with SNR=\Omega(\log n) and measurements scaling as m= \Omega(k \logn/k) for all sparsity levels k satisfying 0 < k \leq \alpha n, where \alpha is a sufficiently small positive constant. Surprisingly, this bound matches the optimal Max-Likelihood performance bounds in terms of SNR, required number of measurements, and admissible sparsity level in an order-wise sense. In contrast to our results, previous results based on LASSO and Max-Correlation techniques either assume significantly larger SNR, sub-linear sparsity levels or restrictive assumptions on signal sets. Our proof technique is based on noisy perturbation of the noiseless \ell_1 problem, in that, we estimate the maximum admissible noise level before sign pattern recovery fails. [ABSTRACT FROM PUBLISHER]

In this paper, we consider the job shop scheduling problem (JSS) with non-anticipatory, per-machine, sequence-dependent setup times (SDST). The contributions of this paper are twofold. First, we propose a formulation in the form of a mixed-integer linear programming (MILP) model to modelize the aforementioned problem. Second, we play a pioneering effort for the effective adaptation of a novel metaheuristic known as electromagnetism-like algorithm (EMA) to solve the foregoing problem under the minimization of makespan. Afterwards, we evaluate the performance of the proposed MILP model, the EMA, and other effective metaheuristic algorithms from the literature on two different sets of benchmarks: small-sized and large-sized instances. The rationale behind applying the MILP model and the other algorithms at the small-sized instances is to compare the solutions obtained by the metaheuristic algorithms and the optimal solutions obtained by the MILP model (optimality gap analysis). Subsequently, to demonstrate the competitiveness of the EMA against some effective algorithms in the literature, we conduct an experimental design based on Taillard's benchmark, which is considered as large-sized instances. The purpose of conducting this very experiment is to show whether the acceptable performance of the EMA is transferrable to large-sized instances. The computational evaluations simply manifest the superiority of our proposed algorithm vs the other high-performing algorithms over both small and large instances. [ABSTRACT FROM AUTHOR]

This paper addresses the complex optimum transformer design problem, which is formulated as a mixed-integer nonlinear programming problem, by introducing an integrated design optimization method based on evolutionary algorithms and numerical electromagnetic and thermal field computations. The main contributions of this research are: i) introduction of a new overall transformer optimization method, minimizing either the overall transformer materials cost or the overall transformer materials and operating cost, ii) expansion of the solution space by innovative techniques that define the variation of crucial design variables such as the conductors' cross-section, ensuring global optimum transformer designs, and iii) incorporation of numerical field computation in order to validate the feasibility of the optimum designs. The proposed method is compared with a heuristic optimization method of the transformer manufacturing industry and the results demonstrate the robustness and the superiority of this new approach. [ABSTRACT FROM AUTHOR]

In this paper, we present two heuristic energy-aware scheduling algorithms-1) Energy Gradient-based Multiprocessor Scheduling (EGMS) algorithm and 2) Energy Gradient-based Multiprocessor Scheduling with Intratask Voltage scaling (EGMSIV) algorithm-for scheduling task precedence graphs in an embedded multiprocessor system having processing elements with dynamic voltage scaling capabilities. Unlike most energy-aware scheduling algorithms that consider task ordering and voltage scaling separately from task mapping, our algorithms consider them in an integrated way. EGMS uses the concept of energy gradient to select tasks to be mapped onto new processors and voltage levels. EGMSIV extends EGMS by introducing intratask voltage scaling using a Linear Programming (LP) formulation to further reduce the energy consumption. Through rigorous simulations, we compare the performance of our proposed algorithms with a few approaches presented in the literature. The results demonstrate that our algorithms are capable of obtaining energy-efficient schedules using less optimization time. On the average, our algorithms produce schedules which consume 10 percent less energy with more than 47 percent reduction in optimization time when compared to a few approaches presented in the literature. In particular, our algorithms perform better in generating energy-efficient schedules for larger task graphs. Our results show a reduction of up to 57 percent in energy consumption for larger task graphs compared to other approaches. [ABSTRACT FROM AUTHOR]

This paper proposes a new algorithm for solving mixed discrete nonlinear programming (MDNLP) problems, designed to efficiently combine particle swarm optimization (PSO), which is a well-known global optimization technique, and branch-and-bound (BB), which is a widely used systematic deterministic algorithm for solving discrete problems. The proposed algorithm combines the global but slow search of PSO with the rapid but local search capabilities of BB, to simultaneously achieve an improved optimization accuracy and a reduced requirement for computational resources. It is capable of handling arbitrary continuous and discrete constraints without the use of a penalty function, which is frequently cumbersome to parameterize. At the same time, it maintains a simple, generic, and easy-to-implement architecture, and it is based on the sequential quadratic programming for solving the NLP subproblems in the BB tree. The performance of the new hybrid PSO-BB architecture algorithm is evaluated against real-world MDNLP benchmark problems, and it is found to be highly competitive compared with existing algorithms. [ABSTRACT FROM AUTHOR]

In this paper, we consider the single machine scheduling problem with linear earliness and quadratic tardiness costs, and no machine idle time. We propose a lower bounding procedure based on the relaxation of the jobs' completion times. Optimal branch-and-bound algorithms are then presented. These algorithms incorporate the proposed lower bound, as well as an insertion-based dominance test. The branch-and-bound procedures are tested on a wide set of randomly generated problems. The computational results show that the branch-and-bound algorithms are capable of optimally solving, within reasonable computation times, instances with up to 20 jobs. [ABSTRACT FROM AUTHOR]

In this paper, an optimization model with a linear objective function subject to a system of fuzzy relation equations, using max-Hamacher product composition operator, is presented. Since its nonempty feasible solution set is in general a nonconvex set, conventional linear programming methods are not suitable to solve such a problem, so an efficient solution procedure for such problems is necessary. In this paper, the feasible solution set of this problem is studied at first. Then, one efficient algorithm (i.e. tabular method algorithm) is proposed in order to solve the problem. Some procedures are also presented to reduce the original problem. Then, the reduced problem is decomposed (if possible) into several sub-problems with smaller dimensions, so solving them becomes very easier by the algorithm. By combining the algorithm and these procedures, another more efficient algorithm is suggested in order to obtain the optimal solution of the original problem. Some numerical examples are also given to illustrate the algorithms. [ABSTRACT FROM AUTHOR]

Recently a new least-squares primal-dual (LSPD) algorithm, that is impervious to degeneracy, has effectively been applied to solving linear programming problems by Barnes et al, 2002. In this paper, we show an application of LSPD to shortest path problems with nonnegative arc length is equivalent to the Dijkstra's algorithm. We also compare the LSPD algorithm with the conventional primal-dual algorithm in solving shortest path problems and show their difference due to degeneracy in solving the 1-1 shortest path problems. [ABSTRACT FROM AUTHOR]

This paper explores optimization of paging and registration policies in cellular networks. Motion is modeled as a discrete-time Markov process, and minimization of the discounted, infinite-horizon average cost is addressed. The structure of jointly optimal paging and registration policies is investigated through the use of dynamic programming for partially observed Markov processes. It is shown that there exist policies with a certain simple form that are jointly optimal. An iterative algorithm for policies with the simple form is proposed and investigated. The algorithm alternates between paging policy optimization, and registration policy optimization. It finds a pair of individually optimal policies. Majorization theory and Riesz's rearrangement inequality are used to show that jointly optimal paging and registration policies are given for symmetric or Gaussian random walk models by the nearest-location-first paging policy and distance threshold registration policies. [ABSTRACT FROM AUTHOR]

The introduction of edge-finding techniques was a significant development in constraint-based scheduling. Today, edge finders are still the state of the art in the disjunctive case and a technique of interest in cumulative scheduling. This paper reconsiders edge-finding algorithms for cumulative scheduling and shows that Nuijten's edge finder, and its derivatives, are incomplete because they use an invalid dominance rule. We then present a correct cumulative edge finder running in time O(n²k), where n is the number of tasks and k the number of different capacity requirements of the tasks. The new algorithm is organized in two phases and first uses dynamic programming to precompute the innermost maximization in the edge-finder specification. The paper also proposes the first extended edge-finding algorithms that run in time O(n²k), improving the running time of available algorithms. Finally, the paper discusses how to speed up the algorithm in practice and how the first phase can be used to improve algorithms based on energetic reasoning. [ABSTRACT FROM AUTHOR]

In this paper, a new efficient algorithm is proposed for the synthesis of low-complexity finite-impulse response (FIR) filters with resource sharing. The original problem statement based on the minimization of signed-power-of-two (SPT) terms has been reformulated to account for the sharable adders. The minimization of common SPT (CSPT) terms that were considered in our proposed algorithm addresses the optimization of the reusability of adders for two major types of common subexpressions, together with the minimization of adders that are needed for the spare SPT terms. The coefficient set is synthesized in two stages. In the first stage, CSPT terms in the vicinity of the scaled and rounded canonical signed digit (CSD) coefficients are allocated to obtain a CSD coefficient set, with the total number of CSPT terms not exceeding the initial coefficient set. The balanced normalized peak ripple magnitude due to the quantization error is fulfilled in the second stage by a local search method. The algorithm uses a common-subexpression-based hamming weight pyramid to seek for low-cost candidate coefficients with preferential consideration of shared common subexpressions. Experimental results demonstrate that our algorithm is capable of synthesizing FIR filters with the least CSPT terms compared with existing filter synthesis algorithms. [ABSTRACT FROM AUTHOR]

Mixed-integer linear programming (MLLP) is a powerful tool for planning and control problems because of its modeling capability and the availability of good solvers. However, for large models, MILP methods suffer computationally. In this paper, we present iterative MILP algorithms that address this issue. We consider trajectory-generation problems with obstacle-avoidance requirements and minimum-time trajectory-generation problems. These problems involve vehicles that are described by mixed logical dynamical equations, a form of hybrid system. The algorithms use fewer binary variables than standard MILP methods, and require less computational effort. [ABSTRACT FROM AUTHOR]

An efficient unambiguous stereo matching technique is presented in this paper. Our main contribution is to introduce a new reliability measure to dynamic programming approaches in general. For stereo vision application, the reliability of a proposed match on a scanline is defined as the cost difference between the globally best disparity assignment that includes the match and the globally best assignment that does not include the match. A reliability-based dynamic programming algorithm is derived accordingly, which can selectively assign disparities to pixels when the corresponding reliabilities exceed a given threshold. The experimental results show that the new approach can produce dense (>70 percent of the unoccluded pixels) and reliable (error rate <0.5 percent) matches efficiently (<0.2 sec on a 2GHz P4) for the four Middlebury stereo data sets. [ABSTRACT FROM AUTHOR]

Motivated by applications in freight handling and open-pit mining, Rhys, Balinski, and Picard studied the problems of selection and closure in papers published in Management Science in 1970 and 1976. They identified efficient algorithms based on linear programming and maximum-flow/minimum-cut procedures to solve these problems. This research has had major impact well beyond the initial applications, reaching across three decades and inspiring work on numerous applications and extensions. The extensions are nontrivial optimization problems that are of theoretical interest. The applications ranged from evolving technologies, image segmentation, revealed preferences, pricing, adjusting utilities for consistencies, just-in-time production, solving certain integer programs in polynomial time, and providing efficient 2-approximation algorithms for a wide variety of hard problems. A recent generalization to a convex objective function has even produced novel solutions to prediction and Bayesian estimation problems. This paper surveys the streams of research stimulated by these papers as an example of the impact of Management Science on the optimization field and an illustration of the far-reaching implications of good original research. [ABSTRACT FROM AUTHOR]

Existing layout-optimization methods for both capacitive and inductive (RLC) crosstalk reduction assume a set of interconnects with a priori given crosstalk bounds in a routing region. RLC crosstalk budgeting is critical for effectively applying these methods at the full-chip level. In this paper, we formulate a full-chip routing optimization problem with RLC crosstalk budgeting, and solve this problem with a multiphase algorithm. In phase I, we solve an optimal RLC crosstalk budgeting based on linear programming to partition crosstalk bounds at sinks into bounds for net segments in routing regions. In phase II, we perform simultaneous shield insertion and net ordering to meet the partitioned crosstalk bounds in each region. In phase III, we carry out a local refinement procedure to reduce the total number of shields. Compared with the best alternative approach in experiments, the proposed algorithm reduces the total routing area by up to 5.71% and uses less runtime. To the best of our knowledge, this work is the first in-depth study on full-chip routing optimization with RLC crosstalk budgeting. [ABSTRACT FROM AUTHOR]

Since Balas extended the classical linear programming problem to the disjunctive programming (DP) problem where the constraints are combinations of both logic AND and OR, many researchers explored this optimization problem under various theoretical or application scenarios such as generalized disjunctive programming (GDP), optimization modulo theories (OMT), robot path planning, real-time systems, etc. However, the possibility of combining these differently-described but form-equivalent problems into a single expression remains overlooked. The contribution of this paper is two folded. First, we convert the linear DP/GDP model, linear-arithmetic OMT problem and related application problems into an equivalent form, referred to as the linear optimization over arithmetic constraint formula (LOACF). Second, a tree-search-based algorithm named RS-LPT is proposed to solve LOACF. RS-LPT exploits the techniques of interval analysis and nonparametric estimation for reducing the search tree and lowering the number of visited nodes. Also, RS-LPT alleviates bad construction of search tree by backtracking and pruning dynamically. We evaluate RS-LPT against two most common DP/GDP methods, three state-of-the-art OMT solvers and the disjunctive transformation based method on optimization benchmarks with different types and scales. Our results favor RS-LPT as compared to existing competing methods, especially for large scale cases. [ABSTRACT FROM AUTHOR]

In this paper, we study Stochastic Composite Optimization (SCO) for sparse learning that aims to learn a sparse solution from a composite function. Most of the recent SCO algorithms have already reached the optimal expected convergence rate \mathcal O(1/\lambda T) , but they often fail to deliver sparse solutions at the end either due to the limited sparsity regularization during stochastic optimization (SO) or due to the limitation in online-to-batch conversion. Even when the objective function is strongly convex, their high probability bounds can only attain \mathcal O(\sqrt\log (1/\delta)/T) with $\delta$ is the failure probability, which is much worse than the expected convergence rate. To address these limitations, we propose a simple yet effective two-phase Stochastic Composite Optimization scheme by adding a novel powerful sparse online-to-batch conversion to the general Stochastic Optimization algorithms. We further develop three concrete algorithms, OptimalSL, LastSL and AverageSL, directly under our scheme to prove the effectiveness of the proposed scheme. Both the theoretical analysis and the experiment results show that our methods can really outperform the existing methods at the ability of sparse learning and at the meantime we can improve the high probability bound to approximately \mathcal {O}(\log (\log (T)/\delta)/\lambda T) . [ABSTRACT FROM AUTHOR]