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The global exponential stability and the exponential convergence rate for time-delay systems with nonlinear uncertainties are investigated. A novel exponential stability criterion for the system is derived using the Lyapunov method. These stability conditions are formulated as linear matrix inequalities (LMIs), which can be easily solved by various convex optimization algorithms. The issue of exponential stability for time-delay systems with nonlinear uncertainties using generalized eigen value problem (GEVP) approach remains open, which motivates this paper. Numerical examples are given to illustrate the usefulness of our proposed method. [ABSTRACT FROM AUTHOR]

In this paper, we consider the convex quadratic optimization problem with simultaneous perturbation in the right-hand side of the constraints and the linear term of the objective function with different parameters. The regions with invariant optimal partitions as well as the behaviour of the optimal value function on the regions are investigated. We show that identifying these regions can be done in polynomial time in the output size. An algorithm for identifying all invariancy regions is presented. Some implementation details as well as a numerical example are discussed. [ABSTRACT FROM AUTHOR]

In this paper we present our experience with the optimization of atomic clusters under the binary Lennard-Jones potential. This is a generalization of the single atom type Lennard-Jones model to the case in which atoms of two different types (and 'sizes') interact within the same cluster. This problem has a combinatorial structure which increases complexity and requires strategies to be revised in order to take into account such new aspects. Our approach has been a very effective one: we have been able not only to confirm most putative optima listed in the Cambridge Cluster Database, but also to find 95 improved solutions. [ABSTRACT FROM AUTHOR]

Different types of underestimation strategies are used in deterministic global optimization. In this paper, convexification and underestimation techniques applicable to problems containing signomial functions are studied. Especially, power transformation and exponential transformation (ET) will be considered in greater detail and some new theoretical results regarding the relation between the negative power transformation and the ET are given. The techniques are, furthermore, illustrated through examples and compared with other underestimating methods used in global optimization solvers such as αBB and BARON. [ABSTRACT FROM AUTHOR]

This paper presents a method for and examples of topology optimization of energy absorption structures. The topology optimization problem is solved by using the elements as design variables. The sensitivity number of an element is derived from using an adjoint method to address two principal design parameters, namely absorbed energy per unit volume, e1, and absorbed energy ratio, e2. Filter techniques are employed to smooth sensitivities in the design space and to eliminate unnecessary structural details below a certain length-scale. The bi-directional evolutionary optimization (BESO) technique is used to search for the optimal design in the whole design domain by gradually removing and adding material. Several examples are presented to demonstrate the capability and effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

We give a direct proof of the fundamental minimization theorem for CVaR presented by Rockafellar and Uryasev in their definitive paper (Conditional value-at-risk for general loss distributions. Journal of Banking and Finance, 26, 1443-1471, 2002). [ABSTRACT FROM AUTHOR]

Site visibility analysis is an important research topic with many applications in Geographical Information Systems. This paper introduces a new paradigm in terrain guarding, called k -guarding. K -guarding is a generalization of the classic guarding problem where, instead of only one guard, each surface patch is guarded by at least k guards. Afterwards, two optimization problems based on k -guarding are defined: an optimum k -guarding, and a constrained k -guarding. There are three heuristic approaches-- k -greedy add, k -stingy drop, and k -reverse greedy--that are proposed as a solution to the above-mentioned optimization problems. The first two are known approaches adapted to k -guarding, while k -reverse greedy is a new, original heuristic. The heuristics are compared using actual topographic surfaces. It is shown that our approach ( k -reverse greedy) gives on average the best near optimum solutions. The most surprising finding of the experiments is that the combination of heuristics introduced here yields even better results. [ABSTRACT FROM AUTHOR]

In incomplete financial markets not every contingent claim can be replicated by a self-financing strategy. The risk of the resulting shortfall can be measured by convex risk measures, recently introduced by Föllmer and Schied (2002). The dynamic optimization problem of finding a self-financing strategy that minimizes the convex risk of the shortfall can be split into a static optimization problem and a representation problem. It follows that the optimal strategy consists in superhedging the modified claim [image omitted] , where H is the payoff of the claim and [image omitted] is a solution of the static optimization problem, an optimal randomized test. In this paper, necessary and sufficient optimality conditions are deduced for the static problem using convex duality methods. The solution of the static optimization problem turns out to be a randomized test with a typical 0-1-structure. [ABSTRACT FROM AUTHOR]

In this paper, we implement Zhang's method [Zhang, S., 2004, Journal of Global Optimization , 29, 479–496], which transforms a general convex optimization problem with smooth convex constraints into a convex conic optimization problem and then apply the techniques of self-dual embedding and central path-following for solving the resulting conic optimization model. A crucial advantage of the approach is that no initial solution is required and the method is particularly suitable when the feasibility status of the problem is unknown. In our implementation, we use a merit function approach proposed by Andersen and Ye [Andersen, E.D. and Ye, Y., 1998, Computational Optimization and Applications , 10, 243–269] to determine the step-size along the search direction. We evaluate the efficiency of the proposed algorithm by observing its performance on some test problems, which include logarithmic functions, exponential functions and quadratic functions in the constraints. Furthermore, we consider in particular the geometric programming and L p -programming problems. Numerical results of our algorithm on these classes of optimization problems are reported. We conclude that the algorithm is stable, efficient and easy-to-use in general. As the method allows the user to freely select the initial solution, it is natural to take advantage of this and apply the so-called warm-start strategy, whenever the data of a new problem is not too much different from a previously solved problem. This strategy turns out to be effective, according to our numerical experience. [ABSTRACT FROM AUTHOR]

The focus of this overview for this issue of Nuclear Technology, which contains papers presented at the American Nuclear Society Advances in Nuclear Fuel Management III (ANFM-III) 2004 topical meeting, is to introduce the subject of nuclear fuel management for light water reactors. A total of 23 papers was presented on this topic at ANFM-III. Nuclear fuel management involves making the so-called out-of-core and in-core decisions. Simply put, the out-of-core decisions address the attributes of the new (fresh) fuel that will be fabricated and the partially burnt (shuffled) fuel to reinsert into the core for additional energy production. The in-core decisions address where the fresh and burnt fuel along with burnable poisons should be located in the core. The above applies to batch refueling strategies, e.g., pressurized water reactors and boiling water reactors (BWRs). For BWRs, additional in-core decisions enter to address control rod pattern paired with core flow rate as a function of burnup. It is obvious that the out-of-core and in-core decisions are coupled. The objective of nuclear fuel management is to minimize the cost of electrical energy generation subject to operational and safety constraints. Since fuel resides in the core for several cycles, a multicycle assessment is required to make nuclear fuel management decisions. For nearly four decades there has been an effort to develop automated computational capability to assist the reload core nuclear design engineer in making nuclear fuel management decisions. This development has ranged from employment of heuristic rules to utilization of mathematical optimization approaches. This overview reviews the development of nuclear fuel management optimization capabilities by first defining the problem, then describing current capabilities, and finally projecting where future capabilities need to be developed to support the needs of reload core nuclear design engineers. [ABSTRACT FROM AUTHOR]

This paper proposes a novel method to select an experimental design for interpolation in simulation. Although the paper focuses on Kriging in deterministic simulation, the method also applies to other types of metamodels (besides Kriging), and to stochastic simulation. The paper focuses on simulations that require much computer time, so it is important to select a design with a small number of observations. The proposed method is therefore sequential. The novelty of the method is that it accounts for the specific input/output function of the particular simulation model at hand; that is, the method is application-driven or customized. This customization is achieved through cross-validation and jackknifing. The new method is tested through two academic applications, which demonstrate that the method indeed gives better results than either sequential designs based on an approximate Kriging prediction variance formula or designs with prefixed sample sizes. [ABSTRACT FROM AUTHOR]

Copyright of INFOR is the property of Taylor & Francis Ltd and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

This paper deals with the optimal production/maintenance (PM) policy for a deteriorating production system which may shift from the in-control state to the out-of-control state while producing items. The process is assumed to have a general shift distribution. Under the commonly used maintenance policy, equal-interval maintenance, the joint optimizations of the PM policy are derived such that the expected total cost per unit time is minimized. Different conditions for optimality, lower and upper bounds and uniqueness properties on the optimal PM policy are provided. The implications of another commonly used policy, to perform a maintenance action only at the end of the production run, are also discussed. Structural properties for the optimal policy are established so that an efficient solution procedure is obtained. In the exponential case, some extensions of the results obtained previously in the literature are presented. A numerical example is provided to illustrate the solution procedure for the optimal production and maintenance policy. [ABSTRACT FROM AUTHOR]

Product lifetime cost is largely determined by product lifetime reliability. In product design, the former is minimized while the latter is treated as a constraint and is usually estimated by statistical means. In this work, a new lifetime cost optimization model is developed where the product lifetime reliability is predicted with computational models derived from physical principles. With the physics-based reliability method, the state of a system is indicated by computational models, and the time-dependent system reliability is then predicted for a given set of distributions and stochastic processes in the model input. A sampling approach to extreme value distributions of input stochastic processes is employed to make the system reliability analysis efficient and accurate. The physics-based reliability analysis is integrated with the lifetime cost model. The integration enables the minimal lifetime costs including those of maintenance and warranty. Two design examples are used to demonstrate the proposed model. [ABSTRACT FROM AUTHOR]

This article presents an effective hybrid cuckoo search and genetic algorithm (HCSGA) for solving engineering design optimization problems involving problem-specific constraints and mixed variables such as integer, discrete and continuous variables. The proposed algorithm, HCSGA, is first applied to 13 standard benchmark constrained optimization functions and subsequently used to solve three well-known design problems reported in the literature. The numerical results obtained by HCSGA show competitive performance with respect to recent algorithms for constrained design optimization problems. [ABSTRACT FROM AUTHOR]

The article presents a case study on mathematics in which theorems are conjectured and proofs are verified. It is stated that the axiomatic method explains how mathematics should be done and uses computers' time inefficiently. It is mentioned that it was found in the study that computer did all the phases of mathematical research all by itself.

We present a numerical bundle-type method for local minimization of a real function of several variables, which is supposed to be locally Lipschitz. We provide a short survey of some optimization algorithms from the literature, which are able to deal with both nonsmoothness and nonconvexity of the objective function. We focus on possible extensions of classical bundle-type methods, originally conceived to deal with convex nonsmooth optimization. They are all based on a convex cutting plane model which has the property of both minorizing everywhere and interpolating at certain points the objective function. Such properties may be lost whenever nonconvexity is present and the case may be described in terms of possible negative values of certain linearization errors. We describe some alternative ways the problem is dealt with in the literature. Here, on the basis of a classification of the limit points of gradient sequences, we define two distinct cutting plane approximations. We derive an algorithm which uses both such models. In particular, only the convex model is primarily adopted to find a tentative displacement from the current stability centre, while the concave one enters into the play only when the convex model has failed in providing a sufficient decrease step. Termination of the method is proved and the results of some numerical experiments are reported. [ABSTRACT FROM AUTHOR]

In many practical applications of nonparametric regression, it is desirable to allow for the possibility that the noise is correlated. In this article, we focus on wavelet-based nonparametric function estimation and propose two distinct methods for estimating the correlation structure of the noise, one based in the time domain and the other based in the wavelet domain. Once the correlation structure has been estimated, there are various methods that may be used for reconstructing the unknown signal; we focus here on the empirical Bayes block shrinkage method proposed by Wang and Wood (2006). A simulation study is described. Our numerical results indicate that the proposed methods do a good job of reconstructing the signal even when the noise is highly correlated. [ABSTRACT FROM AUTHOR]

One of the subjects that undergraduate students learning Object Oriented (OO) design find hard to apply is the construction of class hierarchies in general, and the use of interface classes in particular. The design process requires decomposition and reconstruction of problems in order to model software classes. The common attributes and behaviors are usually modeled using class inheritance except when the common behaviors do not belong to the same class hierarchy; in such case, an interface class is preferred. In order to be able to properly design, the designer has to demonstrate the abstraction abilities on various levels. In this study, we aimed at examining the students' demonstration of abstraction levels during design of class hierarchy in general, and whether or not they use interface classes in particular. The results of the study reveal that a majority of students were able to build a reasonable class hierarchy; however, many of them did not use interface classes as a tool for expressing common behaviors. Nevertheless, all of them could identify and choose the best solution for a particular problem among four different solutions, which included the use of interface class. [ABSTRACT FROM AUTHOR]

We describe a major update of our Matlab freeware GloptiPoly for parsing generalized problems of moments and solving them numerically with semidefinite programming. [ABSTRACT FROM AUTHOR]

This article presents a new multidimensional descent method for solving global optimization problems with box-constraints. This is a hybrid method where local search method is used for a local descent and global search is used for further multidimensional search on the subsets of intersection of cones generated by the local search method and the feasible region. The discrete gradient method is used for local search and the cutting angle method is used for global search. Two- and three-dimensional cones are used for the global search. Such an approach allows one, as a rule, to escape local minimizers which are not global ones. The proposed method is local optimization method with strong global search properties. We present results of numerical experiments using both smooth and non-smooth global optimization test problems. These results demonstrate that the proposed algorithm allows one to find a global or a near global minimizer. [ABSTRACT FROM AUTHOR]

Ant Colony Optimization (ACO) is a class of metaheuristic algorithms sharing the common approach of constructing a solution on the basis of information provided both by a standard constructive heuristic and by previously constructed solutions. This article is composed of three parts. The first one frames ACO in current trends of research on metaheuristics for combinatorial optimization. The second outlines some current research within the ACO community, reporting recent results obtained on different problems, while the third part focuses on a particular research line, named ANTS, providing some details on the algorithm and presenting results recently obtained on a prototypical strongly constrained problem: the set partitioning problem. [ABSTRACT FROM AUTHOR]

The classes of reward-risk optimization problems that arise from different choices of reward and risk measures are considered. In certain examples the generic problem reduces to linear or quadratic programming problems. An algorithm based on a sequence of convex feasibility problems is given for the general quasi-concave ratio problem. Reward-risk ratios that are appropriate in particular for non-normal assets return distributions and are not quasi-concave are also considered. [ABSTRACT FROM AUTHOR]

It has been over ten years since the pioneering work of particle swarm optimization (PSO) espoused by Kennedy and Eberhart. Since then, various modifications, well suited to particular application areas, have been reported widely in the literature. The evolutionary concept of PSO is clear-cut in nature, easy to implement in practice, and computationally efficient in comparison to other evolutionary algorithms. The above-mentioned merits are primarily the motivation of this article to investigate PSO when applied to continuous optimization problems. The performance of conventional PSO on the solution quality and convergence speed deteriorates when the function to be optimized is multimodal or with a large problem size. Toward that end, it is of great practical value to develop a modified particle swarm optimizer suitable for solving high-dimensional, multimodal optimization problems. In the first part of the article, the design of experiments (DOE) has been conducted comprehensively to examine the influences of each parameter in PSO. Based upon the DOE results, a modified PSO algorithm, termed Decreasing-Weight Particle Swarm Optimization (DW-PSO), is addressed. Two performance measures, the success rate and number of function evaluations, are used to evaluate the proposed method. The computational comparisons with the existing PSO algorithms show that DW-PSO exhibits a noticeable advantage, especially when it is performed to solve high-dimensional problems. [ABSTRACT FROM AUTHOR]

We present a new definition of filled function, named globally concavized filled function, for the box constrained continuous global minimization problem. A class of this kind of filled functions are constructed. These functions contain two easily determinable parameters, which are not dependent on the radius of the basin at the current local minimizer to make them be globally concavized filled functions. We design a randomized algorithm to solve the problem basing on these functions and prove that the algorithm can converge asymptotically with probability one to a global minimizer of the problem. Numerical experiments are presented to show the effectiveness and robustness of the algorithm. [ABSTRACT FROM AUTHOR]

There is abundant literature on response surface methodology about how the Nelder–Mead simplex search (NMSS) procedure can be applied to the determination of optimum operating conditions for deterministic response surface functions. However, searching for the optima of stochastic functions seems a more realistic task for many practical situations. This is particularly true when the response surface functions have not been fitted or the physical models may not even exist, so gradient information is not available. In such cases, it might be interesting to employ simplex-search-type methods ‘on-line’ to sequentially optimize the actual response of interest. Toward that end, an enhanced NMSS is proposed in this article to explore the terrains of empirical (or experimental) optimization adaptively where the known response surface function incorporates additional white-noise errors. Internal modifications to basic operations in NMSS are made primarily according to some statistical process control statistics in estimating response variation and confidence bands for mean responses. A series of graphical illustrations are presented to give an insight into the way the new simplex-search-type approach accurately anchors the true optimum point in noisy environments. As evidenced by a wide variety of simulation studies on the published response functions, the new method proves to perform much better than two recent modifications of NMSS in solution quality achieved while applied to the stochastic response surface optimization problems. [ABSTRACT FROM AUTHOR]

Copyright of INFOR is the property of Taylor & Francis Ltd and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Copyright of INFOR is the property of Taylor & Francis Ltd and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

An algorithm for the verification of composite position tolerances is proposed and its computer implementation is described. It is shown that a prevalent graphical verification method does not adequately reflect the standard. Composite position tolerance requirements are mathematically formulated as a non-linear optimization problem with a linear objective function and quadratic constraints. The method of feasible directions is used as the basis for an efficient computer implementation. Its performance is evaluated under various test conditions as well as against a simplex pattern search. [ABSTRACT FROM AUTHOR]