We study a kind of resource allocation models derived from various investment problems, like educational investment, farming investment, industrial investment etc. We will analyze the properties of solutions of the mo...
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We study a kind of resource allocation models derived from various investment problems, like educational investment, farming investment, industrial investment etc. We will analyze the properties of solutions of the models and obtain a polynomial algorithm. We will also apply our theory to a concrete example to demonstrate the algorithm complexity. (C) 2002 Elsevier Inc. All rights reserved.
The authors of this paper recently introduced a transformation [4] that converts a class of semidefinite programs (SDPs) into nonlinear optimization problems free of matrix-valued constraints and variables. This trans...
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The authors of this paper recently introduced a transformation [4] that converts a class of semidefinite programs (SDPs) into nonlinear optimization problems free of matrix-valued constraints and variables. This transformation enables the application of nonlinear optimization techniques to the solution of certain SDPs that are too large for conventional interior-point methods to handle efficiently. Based on the transformation, we proposed a globally convergent, first-order (i.e., gradient-based) log-barrier algorithm for solving a class of linear SDPs. In this paper, we discuss an efficient implementation of the proposed algorithm and report computational results on semidefinite relaxations of three types of combinatorial optimization problems. Our results demonstrate that the proposed algorithm is indeed capable of solving large-scale SDPs and is particularly effective for problems with a large number of constraints.
A practical problem that requires the classification of a set of points of R-n using a criterion not sensitive to bounded outliers is studied in this paper. A fixed-point (k-means) algorithm is defined that uses an ar...
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A practical problem that requires the classification of a set of points of R-n using a criterion not sensitive to bounded outliers is studied in this paper. A fixed-point (k-means) algorithm is defined that uses an arbitrary distance function. Finite convergence is proved. A robust distance defined by Boente et al. is selected for applications. Smooth approximations of this distance are defined and suitable heuristics are introduced to enhance the probability of finding global optimizers. A real-life example is presented and commented. (C) 2002 Elsevier Science B.V., All rights reserved.
A slack-based feasible interior point method is described which can be derived as a modification of infeasible methods. The modification is minor for most line search methods, but trust region methods require special ...
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A slack-based feasible interior point method is described which can be derived as a modification of infeasible methods. The modification is minor for most line search methods, but trust region methods require special attention. It is shown how the Cauchy point, which is often computed in trust region methods, must be modified so that the feasible method is effective for problems containing both equality and inequality constraints. The relationship between slack-based methods and traditional feasible methods is discussed. Numerical results using the KNITRO package show the relative performance of feasible versus infeasible interior point methods.
This paper contributes to the development of the field of augmented Lagrangian multiplier methods for general nonlinear programming by introducing a new update for the multipliers corresponding to inequality constrain...
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This paper contributes to the development of the field of augmented Lagrangian multiplier methods for general nonlinear programming by introducing a new update for the multipliers corresponding to inequality constraints. The update maintains naturally the nonnegativity of the multipliers without the need for a positive-orthant projection, as a result of the verification of the first-order necessary conditions for the minimization of a modified augmented Lagrangian penalty function. In the new multiplier method, the roles of the multipliers are interchanged: the multipliers corresponding to the inequality constraints are updated explicitly, whereas the multipliers corresponding to the equality constraints are approximated implicitly. It is shown that the basic properties of local convergence of the traditional multiplier method are valid also for the proposed method.
The efficiency of adopting lamination parameters as design variables for the reliability-based optimization of a laminated composite plate subject to in-plane loads is presented. The plate failure is evaluated by the ...
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The efficiency of adopting lamination parameters as design variables for the reliability-based optimization of a laminated composite plate subject to in-plane loads is presented. The plate failure is evaluated by the first-ply failure (FPF) criterion, where the ply failure is evaluated based on the Tsai-Wu criterion. According to the FPF criterion, the laminated plate is modeled as a series system consisting of every ply failure. The system reliability of the composite plate is evaluated by Ditlevsen's bounds. Each ply-failure probability is evaluated by the first-order reliability method, where the material properties and applied loads are treated as random variables. As numerical examples, two types of the reliability-based design are formulated in terms of lamination parameters. One is the reliability-maximized design of the constant-thickness plate. The other is the thickness-minimized design under the reliability constraint. Through numerical calculations, it is shown that the reliability has a single peak and a continuous distribution in the lamination parameter space. Consequently, numerical searching rapidly achieves the optimum solution.
This paper presents a formulation of the multicontingency transient stability constrained optimal power flow (MC-TSCOPF) problem and proposes a method to solve it. In the MC-TSCOPF formulation, this paper introduces a...
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This paper presents a formulation of the multicontingency transient stability constrained optimal power flow (MC-TSCOPF) problem and proposes a method to solve it. In the MC-TSCOPF formulation, this paper introduces a modified formulation for integrating transient stability model into conventional OPF, which reduces the calculation load considerably. In our MC-TSCOPF solution, the primal-dual Newton interior point method (IPM) for nonlinear programming (NLP) is adopted. Computation results on the IEEJ WEST10 model system demonstrate the effectiveness of the presented MC-TSCOPF formulation and the efficiency of the proposed solution approach. Moreover, based on quite convincing simulation results, some phenomena occurred when considering multicontingency are elaborated.
nonlinear systems of equations often represent mathematical models of chemical production processes and other engineering problems. Homotopic techniques (in particular, the bounded homotopies introduced by Paloschi) a...
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nonlinear systems of equations often represent mathematical models of chemical production processes and other engineering problems. Homotopic techniques (in particular, the bounded homotopies introduced by Paloschi) are used for enhancing convergence to solutions, especially when a good initial estimate is not available. In this paper, the homotopy curve is considered as the feasible set of a mathematical programming problem, where the objective is to find the optimal value of the homotopic parameter. Inexact restoration techniques can then be used to generate approximations in a neighborhood of the homotopy, the size of which is theoretically justified. Numerical examples are given.
Feasible-points methods have several appealing advantages over the infeasible-points methods for solving equality-constrained nonlinear optimization problems. The known feasible-points methods however solve, often lar...
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Feasible-points methods have several appealing advantages over the infeasible-points methods for solving equality-constrained nonlinear optimization problems. The known feasible-points methods however solve, often large, systems of nonlinear constraint equations in each step in order to maintain feasibility. Solving nonlinear equations in each step not only slows down the algorithms considerably, but also the large amount of floating-point computation involved introduces considerable numerical inaccuracy into the overall computation. As a result, the commercial software packages for equality-constrained optimization are slow and not numerically robust. We present a radically new approach to maintaining feasibility-called the canonical coordinates method (CCM). The CCM, unlike previous methods, does not adhere to the coordinate system used in the problem specification. Rather, as the algorithm progresses CCM dynamically chooses, in each step, a coordinate system that is most appropriate for describing the local geometry around the current iterate. By dynamically changing the coordinate system to suit the local geometry, the CCM is able to maintain feasibility in equality-constrained nonlinear optimization without having to solve systems of nonlinear equations. We describe the CCM and present a proof of its convergence. We also present a few numerical examples which show that CCM can solve, in very few iterations, problems that cannot be solved using the commercial NLP solver in MATLAB 6.1. (C) 2002 Published by Elsevier Science Inc.
Software testing is a very important phase of the software development process. It is a very difficult job for a software manager to allocate optimally the financial budget to a software project during testing. In thi...
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Software testing is a very important phase of the software development process. It is a very difficult job for a software manager to allocate optimally the financial budget to a software project during testing. In this paper the problem of optimal allocation of the software testing cost is studied. There exist several models focused on the development of software costs measuring the number of software errors remaining in the software during testing. The purpose of this paper is to use these models to formulate the optimization problems of resource allocation: Minimization of the total number of software errors remaining in the system. On the assumption that a software project consists of some independent modules, the presented approach extends previous work by defining new goal functions and extending the primary assumption and precondition.
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