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In this paper, two modified spectral conjugate gradient methods which satisfy sufficient descent property are developed for unconstrained optimization problems. For uniformly convex problems, the first modified spectral type of conjugate gradient algorithm is proposed under the Wolfe line search rule. Moreover, the search direction of the modified spectral conjugate gradient method is sufficiently descent for uniformly convex functions. Furthermore, according to the Dai-Liao's conjugate condition, the second spectral type of conjugate gradient algorithm can generate some sufficient decent direction at each iteration for general functions. Therefore, the second method could be considered as a modification version of the Dai-Liao's algorithm. Under the suitable conditions, the proposed algorithms are globally convergent for uniformly convex functions and general functions. The numerical results show that the approaches presented in this paper are feasible and efficient. [ABSTRACT FROM AUTHOR]

During the past decade, solving complex optimization problems with metaheuristic algorithms has received considerable attention among practitioners and researchers. Hence, many metaheuristic algorithms have been developed over the last years. Many of these algorithms are inspired by various phenomena of nature. Evolutionary intelligence is a research field that models the behaviour of insects or animals. Several algorithms arising from such models have been proposed to solve a wide range of complicated optimizable systems. In this paper, a novel evolutionary technique called Artificial Spider Algorithm (ASA) for solving optimization tasks in unconstrained problems with high nonlinearity is proposed. The ASA is based on the simulation of spider behaviour. For this purpose, a new metaphysical method according to spinning web and hunting insects via spider is inspired in nature. In order to illustrate the proficiency of the proposed approach, it is compared to other well-known evolutionary methods. The comparison investigates several test functions that are commonly considered within the literature of evolutionary algorithms. The result shows a high performance and effectiveness of this method for searching a global optimum, as well as the cost reduction noticeably for various benchmark functions. [ABSTRACT FROM AUTHOR]

Following some recent research about fractional programming problems with absolute-value functions, in this paper, we consider this class of optimization problems. In the related literature, there exists a famous transformation which is used to convert the above-mentioned nonsmooth fractional optimization problem into a smooth one. This work presents some conditions under which the considered nonsmooth problem can fail to be equivalent to the obtained smooth one. [ABSTRACT FROM AUTHOR]

In this paper, based on the 3-1 piecewise nonlinear complementarity problem (NCP) function, we proposed a smoothing Newton-type method for the generalized nonlinear complementarity problem (GNCP) with a modified non-monotone line search. The algorithm for a GNCP is more difficult than that for an NCP, because two functions must be considered in the problem. We reformulate the (GNCP) to a smoothing system of equations by two independent variables, and then develop a smoothing Newton-type method for solving it. Under reasonable conditions, we obtain the global convergent properties. Also, the numerical experiments are reported in this paper. [ABSTRACT FROM AUTHOR]

This paper describes the methods for finding fast algorithms for computing matrix–vector products including the procedures based on the block-structured matrices. The proposed methods involve an analysis of the structural properties of matrices. The presented approaches are based on the well-known optimization techniques: the simulated annealing and the hill-climbing algorithm along with its several extensions. The main idea of the proposed methods consists in finding a decomposition of the original matrix into a sparse matrix and a matrix corresponding to an appropriate block-structured pattern. The main criterion for optimizing is a reduction of the computational cost. The methods presented in this paper can be successfully implemented in many digital signal processing tasks. [ABSTRACT FROM PUBLISHER]

Renewable energies and, in particular, wind power have come to the forefront in the electricity market in recent years. The main drawback of wind power generation, however, is the major difficulty in forecasting its production. For this reason, when wind farms go to the market, they are very often made to pay penalties for the deviations between forecasting and actual production. In this paper we shall analyse whether real-time compensation of wind power plant deviation penalties is profitable by means of the coordinated optimization of the wind power plant with a large pumped-storage hydro-plant. We shall model the pumped storage plant in great detail and make use of optimal control techniques to carry out the optimization. We shall analyse the most relevant recent papers on the subject and compare them with our technique. We shall also analyse another possible solution based on compensation carried out a posteriori, instead of in real time. [ABSTRACT FROM PUBLISHER]

This paper establishes a theoretical framework of infeasible Mehrotra-type predictor-corrector algorithm for Cartesian nonlinear complementarity problems over symmetric cones which can be regarded as an extension of Liu et al. [Polynomial convergence of Mehrotra-type predictor-corrector algorithm for the Cartesian -LCP over symmetric cones, Optimization 64(4) (2013), pp. 1-23] for Cartesian linear complementarity problems over symmetric cones to Cartesian nonlinear complementarity problems over symmetric cones. The iteration complexities of the proposed algorithm are estimated and some numerical results are provided. The numerical results show that the proposed algorithm is efficient and reliable. [ABSTRACT FROM AUTHOR]

This paper proposes a nonmonotone scaled conjugate gradient algorithm for solving large-scale unconstrained optimization problems, which combines the idea of scaled memoryless Broyden-Fletcher-Goldfarb-Shanno preconditioned conjugate gradient method with the nonmonotone technique. An attractive property of the proposed method is that the search direction always provides sufficient descent step at each iteration. This property is independent of the line search used. Under appropriate assumptions, the method is proven to possess global convergence for nonconvex smooth functions, and R-linear convergence for strongly convex functions. Preliminary numerical results and related comparisons show the efficiency of the proposed method in practical computation. [ABSTRACT FROM AUTHOR]

In the supply chain, most businesses in the pre-order penetration point (pre-OPP) operate under the forecast-driven mode, so that the decisions regarding inventory are made in accordance with the forecast and replenishment planning. This paper considers the stochastic dynamic lot-sizing problem of the two-phased transportation cost, service level constraint, and cash flow under a non-deterministic demand. This problem includes a nonlinear integer programming sub-problem. Therefore, this paper proposes an optimisation replenishment policy method based on modified ant colony optimisation (ACO) and response surface methodology. The main differences between the modified ACO and the traditional ACO lie in the modified update of pheromone intensity and the dynamic mutation operator. The experimental result shows that when the demand is normal distribution, the proposed approach, successfully finds the stationary point of minimum response. Besides, in the test of the algorithm solution quality, the modified ACO is better than the traditional ACO in all scenarios. [ABSTRACT FROM AUTHOR]

Affective computing is important to the human–computer interaction, while facial expression analysis is the core issue. In this paper, a multi-model approach is proposed to achieve rational and satisfactory results for real-time facial expression analysis. With the advantages of multi-model interaction, the traditional process of cluster construction is optimized for the facial expression cluster structures according to the multi-model selection, distribution and evaluation interactions. Experiments are conducted to evaluate the rationality of the multi-model approach outlined in this paper. The satisfactory results demonstrate favourable performance comparable to the best results achieved through the cooperative neuron-computing interactions. Not only can the resultant approach construct the cluster distribution efficiently and accurately, but also it is capable of achieving high-quality and high-convergence interactive computing. [ABSTRACT FROM PUBLISHER]

This paper presents a deterministic global optimization algorithm for solving minimax linear fractional programming (MLFP). In this algorithm, a new linearization technique is proposed, which uses more information of the objective function of the (MLFP) than other techniques. By utilizing this new linearization technique, the initial nonconvex programming problem (MLFP) is reduced to a sequence of linear relaxation programming (LRP) problems, which can provide reliable lower bound of the optimal value. The proposed algorithm is convergent to the global minimum of the (MLFP) through the successive refinement of the feasible region and solutions of a series of the (LRP). Compared with the known algorithms, numerical results show that the proposed algorithm is robust and effective. [ABSTRACT FROM PUBLISHER]

The lown-rank tensor recovery problem is an interesting extension of thecompressed sensing. This problem consists of finding a tensor of minimumn-rank subject to linear equality constraints and has been proposed in many areas such as data mining, machine learning and computer vision. In this paper, operator splitting technique and convex relaxation technique are adapted to transform the lown-rank tensor recovery problem into a convex, unconstrained optimization problem, in which the objective function is the sum of a convex smooth function with Lipschitz continuous gradient and a convex function on a set of matrices. Furthermore, in order to solve the unconstrained nonsmooth convex optimization problem, an accelerated proximal gradient algorithm is proposed. Then, some computational techniques are used to improve the algorithm. At the end of this paper, some preliminary numerical results demonstrate the potential value and application of the tensor as well as the efficiency of the proposed algorithm. [ABSTRACT FROM PUBLISHER]

This paper presents a method to solve the economic dispatch (ED) problem for thermal unit systems involving combined cycle (CC) units. The ED problem finds the optimal generation of each unit in order to minimize the total generation cost while satisfying the total demand and generating-capacity constraints. A CC unit presents multiple configurations or states, each state having its own unique cost curve. Therefore, in performing ED, we need to be able to shift between these cost curves. Moreover, the cost curve is not convex for some of these states. Hence, ED becomes a non-convex optimization problem, which is difficult to solve by conventional methods. In this paper we present a new technique, developed to find the global solution, that is based on the calculation of the infimal convolution. The paper includes the results for a case test and we compare our solution with other techniques. [ABSTRACT FROM PUBLISHER]

The efficiency of the classic alternating direction method of multipliers has been exhibited by various applications for large-scale separable optimization problems, both for convex objective functions and for nonconvex objective functions. While there are a lot of convergence analysis for the convex case, the nonconvex case is still an open problem and the research for this case is in its infancy. In this paper, we give a partial answer on this problem. Specially, under the assumption that the associated function satisfies the Kurdyka–Łojasiewicz inequality, we prove that the iterative sequence generated by the alternating direction method converges to a critical point of the problem, provided that the penalty parameter is greater than 2L, whereLis the Lipschitz constant of the gradient of one of the involved functions. Under some further conditions on the problem's data, we also analyse the convergence rate of the algorithm. [ABSTRACT FROM AUTHOR]

Existing literature on multicast routing protocols in wireless mesh networks (WMNs) from the view point of the links involved in routing are divided into two categories: schemes are aimed at multicast construction with minimal interference which is known as NP hard problem. In contrast, other methods develop network-coding-based solutions with the main objective of throughput maximization, which can effectively reduce the complexity of finding the optimal routing solution from exponential to polynomial time. The proposed framework in this paper is placed in the second category. In multi-channel multi-radio WMNs (MCMR WMNs), each node is equipped with multiple radios, each tuned on a different channel. In this paper, for the first time, we propose a cross-layer convex optimization framework for joint channel assignment and multicast throughput maximization in MCMR WMNs. The proposed method is composed of two phases: in the first phase, using cellular learning automata, channels are assigned to the links established between the radios of the nodes in a distributed fashion such that the minimal interference coefficient for each link is provided. Then, the resultant channel assignment scheme is utilized in the second phase for throughput maximization within an iterative optimization framework based on Lagrange relaxation and primal problem decomposition. We have conducted many experiments to contrast the performance of our solution against many representative approaches. [ABSTRACT FROM AUTHOR]

This paper considers the delay-dependent stability problem of recurrent neural networks with interval time-varying delays. An appropriate Lyapunov–Krasovskii functional is constructed and the combination method of Wirtinger inequality and reciprocally convex optimization technique is employed. Combing a new activation function segmentation method of the boundary condition and the orthogonal complement lemma, three further improved delay-dependent stability criteria are established. Finally, two numerical examples show the effectiveness of our proposed method by comparison with the recent existing works. [ABSTRACT FROM AUTHOR]

This paper describes iterative methods for solving the general linear matrix equation including the well-known Lyapunov matrix equation, Sylvester matrix equation and some related matrix equations encountered in control system theory, as special cases. We develop the methods from the optimization point of view in the sense that the iterative algorithms are constructed to solve some optimization problems whose solutions are closely related to the unique solution to the linear matrix equation. Actually, two optimization problems are considered and, therefore, two iterative algorithms are proposed to solve the linear matrix equation. To solve the two optimization problems, the steepest descent method is adopted. By means of the so-called weighted inner product that is defined and studied in this paper, the convergence properties of the algorithms are analysed. It is shown that the algorithms converge at least linearly for arbitrary initial conditions. The proposed approaches are expected to be numerically reliable as only matrix manipulation is required. Numerical examples show the effectiveness of the proposed algorithms. [ABSTRACT FROM AUTHOR]

In this paper, we consider a kernel-based online learning algorithm for regression when the sampling process is unbounded. Under a moment hypothesis on the sampling outputs, we provide a confidence-based bound for the error in the corresponding reproducing kernel Hilbert space. [ABSTRACT FROM AUTHOR]

Communication networks are immensely important today, since both companies and individuals use numerous services that rely on them. This paper considers the design of hierarchical (communication) networks. We consider the survivability of asymmetrical hierarchical network flows (AHNF), when arcs failure and, hence, flow destruction is probable. In such networks, it is supposed that the remaining arc capacities are known and the guaranteed evaluation of the functional capability assumes finding the worst distribution of flow in the destructed network. Since, in the network flows, a unique efficiency criterion is not generally known or defined, we assess the quality of the network functioning by a measure of demands satisfaction, i.e. the fraction of satisfied demands at the sink nodes. With regard to this criterion, we construct the mathematical model of the network regardless of the design structure. Then, by defining a measure of satisfying the demands, we compute and compare the survivability of two well-known reserve designs, namely radial and circular reserves. [ABSTRACT FROM AUTHOR]

In this paper, we present the general bounds of multiplicative relative perturbation for diagonalizable matrices, which are the improvement of recent results. The bounds gained here are sharper than those in related literatures. In addition, we obtain the multiplicative relative bounds for normal matrices, which are discussed first. [ABSTRACT FROM AUTHOR]

A data mining algorithm, such as Apriori, discovers a huge number of association rules (ARs) and therefore efficiently ranking all these rules is an important issue. This paper suggests a data envelopment analysis (DEA) method for ranking the discovered ARs using a maximum discrimination between the interestingness criteria defined for all ARs. It is shown that the proposed DEA model has a unique optimal solution which can be computed efficiently when the maximum discrimination between the criteria, the difference between DEA weights, is considered. The contribution of this study can be explained as follows: First, we show that using the conventional DEA model for ranking ARs may produce an invalid result because the weights corresponding to interestingness criteria would not discriminate between the criteria. This is investigated for a dataset consisting of 46 ARs with four criteria, namely support, confidence, itemset value and cross-selling. The paper also introduces the maximum discrimination between the weights of the criteria and obtains the optimal solution of the corresponding DEA model efficiently without the need of solving the related mathematical models. On the other hand, this model concludes less number of useful rule(s). A comparative analysis is then used to show the advantage of the proposed DEA method. [ABSTRACT FROM AUTHOR]

This paper deals with the optimal control (OC) problem that arise when a hydraulic system with fixed-head hydroplants is considered. In the frame of a deregulated electricity market, the resulting Hamiltonian for such OC problems is linear in the control variable and results in an optimal singular/bang-bang control policy. To avoid difficulties associated with the computation of optimal singular/bang-bang controls, an efficient and simple optimization algorithm is proposed. The computational technique is illustrated on one example. [ABSTRACT FROM AUTHOR]

For the global optimization problems with continuous variables, evolutionary algorithms (EAs) are often used to find the approximate solutions. The number of generations for an EA to find the approximate solutions, called the first hitting time, is an important index to measure the performance of the EA. However, calculating the first hitting time is still difficult in theory. This paper proposes some new drift conditions that are used to estimate the upper bound of the first hitting times of EAs for finding the approximate solutions. Two case studies are given to show how to apply these conditions to estimate the first hitting times. [ABSTRACT FROM AUTHOR]

Some factories use the cutting and stamping processes to divide stock plates into circles to make products. A guillotine machine cuts the plate into strips in the cutting process and then a stamping press punches out circles from the strips in the stamping process. The circles in a strip have the same size. The number of rows of circles in each strip is limited. Under these constraints, this paper addresses the following primary objective: to cut a plate by a guillotine method so that the maximal number of circles is obtained. Then the secondary objective should be optimized: the cutting layout should use a minimal number of strips. The problem is formulated as a bi-objective optimization problem and a recursive algorithm is presented for it. The computational results indicate that the algorithm can efficiently simplify the cutting process. [ABSTRACT FROM AUTHOR]

Principal component analysis (PCA) is well recognized in dimensionality reduction, and kernel PCA (KPCA) has also been proposed in statistical data analysis. However, KPCA fails to detect the nonlinear structure of data well when outliers exist. To reduce this problem, this paper presents a novel algorithm, named iterative robust KPCA (IRKPCA). IRKPCA works well in dealing with outliers, and can be carried out in an iterative manner, which makes it suitable to process incremental input data. As in the traditional robust PCA (RPCA), a binary field is employed for characterizing the outlier process, and the optimization problem is formulated as maximizing marginal distribution of a Gibbs distribution. In this paper, this optimization problem is solved by stochastic gradient descent techniques. In IRKPCA, the outlier process is in a high-dimensional feature space, and therefore kernel trick is used. IRKPCA can be regarded as a kernelized version of RPCA and a robust form of kernel Hebbian algorithm. Experimental results on synthetic data demonstrate the effectiveness of IRKPCA. [ABSTRACT FROM AUTHOR]

Multigrid methods have been proven to be an efficient approach in accelerating the convergence rate of numerical algorithms for solving partial differential equations. This paper investigates whether multigrid methods are helpful to accelerate the convergence rate of evolutionary algorithms for solving global optimization problems. A novel multigrid evolutionary algorithm is proposed and its convergence is proven. The algorithm is tested on a set of 13 well-known benchmark functions. Experiment results demonstrate that multigrid methods can accelerate the convergence rate of evolutionary algorithms and improve their performance. [ABSTRACT FROM AUTHOR]

In this paper, the new short-term problems that are faced by a generation company in a deregulated electricity market are addressed and an optimization algorithm is proposed. Our model of the spot market explicitly represents the price of electricity as an uncertain exogenous variable. We consider a very complex problem of hydrothermal optimization with pumped-storage plants, so the problem deals with non-regular Lagrangian and non-holonomic inequality constraints. To obtain a necessary minimum condition, the problem was formulated within the framework of nonsmooth analysis using the generalized (or Clarke's) gradient and the Nonsmooth maximum principle. The optimal control problem is solved by means of an algorithm implemented in the commercial software package Mathematica. Results of the application of the method to a numerical example are presented. [ABSTRACT FROM AUTHOR]

This paper presents the nonlinear optimal control for the deployment process of an elastically tethered subsatellite model, which involves not only the usually addressed in-plane motion, but also the out-of-plane motion. All the nonlinearities in the system model and the mission-related state-control constraints are taken into consideration. Instead of the commonly used state-space model, a second-order differential inclusion formulation is exploited in this paper to achieve a significant reduction of the number of system variables. The optimal control is solved by discretizing the optimal control problem first and then solving the resulting large-scale optimization problem. The case studies in the paper demonstrate well the performance of the proposed strategy. [ABSTRACT FROM AUTHOR]

This paper presents an environmentally constrained economic dispatch algorithm for a hydrothermal system within the framework of a competitive and deregulated electricity market. The optimization problem of a firm in a competitive market is described, the objective function of which can be defined as profit maximization, and we consider that thermal plants are constrained to technical and environmental restrictions. An optimal control technique is applied and Pontryagin's theorem is employed. The proposed algorithm is implemented using the Mathematica© package and is applied to a sample system. [ABSTRACT FROM AUTHOR]

Bayesian network is an effective representation tool to describe the uncertainty of the knowledge in artificial intelligence. One important method to learning Bayesian network from data is to employ a search procedure to explore the space of networks and a scoring metric to evaluate each candidate structure. In this paper, a novel discrete particle swarm optimization algorithm has been designed to solve the problem of Bayesian network structures learning. The proposed algorithm not only maintains the search advantages of the classical particle swarm optimization but also matches the characteristics of Bayesian networks. Meanwhile, mutation and neighbor searching operators have been used to overcome the drawback of premature convergence and balance the exploration and exploitation abilities of the particle swarm optimization. The experimental results on benchmark networks illustrate the feasibility and effectiveness of the proposed algorithm, and the comparative experiments indicate that our algorithm is highly competitive compared to other algorithms. [ABSTRACT FROM AUTHOR]

In this paper, we introduce a new algorithm for solving nonlinear programming (NLP) problems. It is an extension of Guo's algorithm [1] which possesses enhanced capabilities for solving NLP problems. These capabilities include: a) extending the variable subspace, b) adding a search process over subspaces and normalized constraints, c) using an adaptive penalty function, and d) adding the ability to deal with integer NLP problems, 0-1 NLP problems, and mixed-integer NLP problems which have equality constraints. These four enhancements increase the capabilities of the algorithm to solve nonlinear programming problems in a more robust and universal way. This paper will present results of numerical experiments which show that the new algorithm is not only more robust and universal than its competitors, but also its performance level is higher than any others in the literature. [ABSTRACT FROM AUTHOR]

A class of large-scale linear control systems, where the overall objective function is a nonlinear function of multiple quadratic performance indices, is investigated in this paper. Chebyshev spectral approximation technique is used for state and control variables. Numerical example has been given at the end of this paper. [ABSTRACT FROM AUTHOR]

Many engineering and scientific problems need to solve boundary value problems for partial differential equations or systems of them. For most cases, to obtain the solution with desired precision and in acceptable time, the only practical way is to harness the power of parallel processing. In this paper, we present some effective applications of parallel processing based on hybrid CPU/GPU domain decomposition method. Within the family of domain decomposition methods, the so-called optimized Schwarz methods have proven to have good convergence behaviour compared to classical Schwarz methods. The price for this feature is the need to transfer more physical information between subdomain interfaces. For solving large systems of linear algebraic equations resulting from the finite element discretization of the subproblem for each subdomain, Krylov method is often a good choice. Since the overall efficiency of such methods depends on effective calculation of sparse matrix–vector product, approaches that use graphics processing unit (GPU) instead of central processing unit (CPU) for such task look very promising. In this paper, we discuss effective implementation of algebraic operations for iterative Krylov methods on GPU. In order to ensure good performance for the non-overlapping Schwarz method, we propose to use optimized conditions obtained by a stochastic technique based on the covariance matrix adaptation evolution strategy. The performance, robustness, and accuracy of the proposed approach are demonstrated for the solution of the gravitational potential equation for the data acquired from the geological survey of Chicxulub crater. [ABSTRACT FROM AUTHOR]

In this paper, a finite filter is used in the structure of the Barzilai–Browein (BB) gradient method in order to propose a new modified BB algorithm for solving large-scale unconstrained optimization problems. Our algorithm is equipped with a relaxed nonmonotone line search technique which allows the algorithm to enjoy the nonmonotonicity properties from scratch. Under some suitable conditions, the global convergence property of the new proposed algorithm is established. Numerical results on some test problems in CUTEr library show the efficiency and effectiveness of the new algorithm in practice too. [ABSTRACT FROM PUBLISHER]

In the literature, there are a few researches to design some parameters in the proximal point algorithm (PPA), especially for the multi-objective convex optimizations. Introducing some parameters to PPA can make it more flexible and attractive. Mainly motivated by our recent work [Bai et al. A parameterized proximal point algorithm for separable convex optimization. Optim Lett. (2017) doi:10.1007/s11590-017-1195-9], in this paper we develop a general parameterized PPA with a relaxation step for solving the multi-block separable structured convex programming. By making use of the variational inequality and some mathematical identities, the global convergence and the worst-case convergence rate of the proposed algorithm are established. Preliminary numerical experiments on solving a sparse matrix minimization problem from statistical learning validate that our algorithm is more efficient than several state-of-the-art algorithms. [ABSTRACT FROM AUTHOR]

Based on the Moreau–Yosida regularization and a modified line search technique, this paper presents an implementable memory gradient method for solving a possibly non-differentiable convex minimization problem by converting the original objective function to a once continuously differentiable function. A main feature of this proposed method is that at each iteration, it sufficiently uses the previous multi-step iterative information and avoids the storage and computation of some matrices. Moreover, the proposed method makes use of approximate function and gradient values of the Moreau–Yosida regularization instead of the corresponding exact values. Under reasonable conditions, the convergence properties of the proposed algorithm are analysed. Preliminary numerical results show that the proposed method is efficient and can be applied to solve large-scale non-smooth optimization problems. [ABSTRACT FROM AUTHOR]

In this paper, saddle point criteria and Wolfe duality theorems are established for a new class of nondifferentiable vector optimization problems with inequality and equality constraints. The results are proved under nondifferentiable (Φ, ρ)-invexity and related scalar and vector-valued Lagrangians defined for the considered nonsmooth multiobjective programming problem. It turns out that the results are established for such vector optimization problems in which not all functions constituting a vector optimization problem possess the fundamental property of invexity and the most of generalized invexity notions previously defined in the literature. [ABSTRACT FROM PUBLISHER]

Firefly algorithm is a bio-inspired optimization algorithm which has been empirically demonstrated to perform well on many optimization problems. However, it can easily get trapped in the local optima and causes low precision. Therefore, improvement of this disadvantage is the very important. In this paper, we propose a wise strategy for step setting, which considers the information of firefly's personal and the global best positions. The results show that the modified algorithm enhances the performance of the basic firefly algorithm. [ABSTRACT FROM PUBLISHER]

This paper proposes an affine scaling interior trust-region method in association with nonmonotone line search filter technique for solving nonlinear optimization problems subject to linear inequality constraints. Based on a Newton step which is derived from the complementarity conditions of linear inequality constrained optimization, a trust-region subproblem subject only to an ellipsoidal constraint is defined by minimizing a quadratic model with an appropriate quadratic function and scaling matrix. The nonmonotone schemes combining with trust-region strategy and line search filter technique can bring about speeding up the convergence progress in the case of high nonlinear. A new backtracking relevance condition is given which assures global convergence without using the switching condition used in the traditional line search filter technique. The fast local convergence rate of the proposed algorithm is achieved which is not depending on any external restoration procedure. The preliminary numerical experiments are reported to show effectiveness of the proposed algorithm. [ABSTRACT FROM AUTHOR]

Many real world problems can be modelled as optimization problems. However, the traditional algorithms for these problems often encounter the problem of being trapped in local minima. The filled function method is an effective approach to tackle this kind of problems. However the existing filled functions have the disadvantages of discontinuity, non-differentiability or sensitivity to parameters which limit their efficiency. In this paper, we proposed a new filled function which is continuous and differentiable without any parameter to tune. Compared to discontinuous or non-differentiable filled functions, the continuous and differentiable filled function mainly has three advantages: firstly, it is not easier to produce extra local minima, secondly, more efficient local search algorithms using gradient information can be applied and thirdly, a continuous and differentiable filled function can be optimized more easily. Based on the new proposed filled function, a new algorithm was designed for unconstrained global optimization problems. Numerical experiments were conducted and the results show the proposed algorithm was more efficient. [ABSTRACT FROM PUBLISHER]

In this paper, a family of new fourth-order optimal iterative methods for solving nonlinear equations is proposed. The classical King's family of fourth-order schemes is obtained as an special case. We also present results for describing the conjugacy classes and dynamics of some of the presented methods for complex polynomials of different degrees. [ABSTRACT FROM PUBLISHER]

In this paper, the least-squares solutions of constrained inverse eigenvalue problem and the associated optimal approximation problem are considered. We get the general expression of the least-squares solutions of the constrained inverse eigenvalue problem, obtain the representation of the unique optimal approximation solution in the least-squares solutions set, and give the algorithm and corresponding computational examples. [ABSTRACT FROM PUBLISHER]

The r-component connectivity κ r (G) of the non-complete graph G is the minimum number of vertices whose deletion results in a graph with at least r components. So, κ2 is the usual connectivity. In this paper, we determine the r-component connectivity of the hypercube Q n for r=2, 3, …, n+1, and we classify all the corresponding optimal solutions. [ABSTRACT FROM PUBLISHER]

In this paper, we design and analyse an infeasible interior-point algorithm based on a simple function for linear optimization. The infeasible algorithm contains two types of search directions: the feasibility search direction and the centrality search direction. Both of the directions are determined by the simple function. The algorithm uses full step, thus no need to perform the line-search procedure. Although the proposed function is simple, as it will be shown, the induced infeasible algorithm enjoys the best-known iteration complexity for infeasible interior-point algorithm. [ABSTRACT FROM AUTHOR]

The paper studies the extension problem of continuous maps between axiomatic locally finite spaces (for short, ALF spaces). Indeed, an ALF space is a topological space satisfying a set of axioms suggested in Kovalevsky [Axiomatic digital topology, J. Math. Imag. Vis. 26 (2006), pp. 41–58; Geometry of Locally Finite Spaces, Monograph, Berlin, 2008]. Further, an ALF space is defined by using a special kind of neighbourhood different from the topological neighbourhood in classical topology so that the continuity of maps between ALF spaces can be defined by preserving the neighbourhood relation (see Definition 10). Therefore, it is necessary to develop the notions of continuity, homeomorphism and local homeomorphism for such spaces by using the neighbourhood relation, which can be applicable in computer science. In the study of a deformation of an ALF space, we can develop a special kind of retract on ALF spaces. By using the retract, we can efficiently deal with the extension of continuous maps between ALF spaces. [ABSTRACT FROM AUTHOR]

In this paper, we introduce a new technique based on cubic exponential spline functions for computing approximations to the solution of a system of fourth-order boundary value problems associated with obstacle, unilateral and contact problems. It is shown that the present method is of order two and four and gives approximations which are better than those produced by other collocation, finite difference and spline methods. Numerical evidence is presented to illustrate the applicability of the new methods. [ABSTRACT FROM AUTHOR]

This paper considers an M/M/r queueing system with infinite capacity, in which the number of working servers changes depending on the queue length. The steady-state probability distributions and the expected number of customers in the system are derived, which are used to construct a cost function. In order to minimize the expected cost of the system, we use the genetic algorithm to find the best thresholds of queue length in activating servers and their corresponding service rate. Some illustrative examples are provided to demonstrate how the process of this algorithm works for the optimal management policy of the multi-server queueing system. [ABSTRACT FROM AUTHOR]

In this paper, we discuss modelling and solving some multiobjective optimization problems arising in biology. A class of comparison problems for string selection in molecular biology and a relocation problem in conservation biology are modelled as multiobjective optimization programmes. Some discussions about applications, solvability and different variants of the obtained models are given, as well. A crucial part of the study is based upon the Pareto optimization which refers to the Pareto solutions of multiobjective optimization problems. For such solution, improvement of some objective function can only be obtained at the expense of the deterioration of at least one other objective function. [ABSTRACT FROM AUTHOR]

This paper presents a method for finding the optimal control of linear systems with delays in state and input and the quadratic cost functional using an orthonormal basis for square integrable functions. The state and control variables and their delays are expanded in an orthonormal basis with unknown coefficients. Using operational matrices of integration, delay and product, the relation between coefficients of variables is provided. Then, necessary condition of optimality is driven as a linear system of algebraic equations in terms of the unknown coefficients of state and control variables. As an application of this method, the linear Legendre multiwavelets as an orthonormal basis for L2[0, 1] are used. Two time-delayed optimal control problems are approximated to establish the usefulness of the method. [ABSTRACT FROM AUTHOR]

This paper studies the eigenvalue optimization problems in the shape design of the two-density inhomogeneous materials. Two types of greedy algorithms are proposed to solve three optimization problems in finite element discretization. In the first type, the whole domain is initialized by one density. For each problem of the eigenvalue optimizations, we define a measurement of the element, which is the criterion to determine the 'best' element. We change the density of the 'best' element to the other density. Then the algorithm repeats the procedure until the area constraint is satisfied. In the second type, the algorithm begins with the density distribution satisfying the area constraint. Also, according to the measurement of the element, the algorithm finds a pair of the 'best' elements and exchanges their densities between each other. Furthermore, the accelerating greedy algorithms are proposed to speed up both two types. Three numerical examples are provided to illustrate the results. [ABSTRACT FROM AUTHOR]