Equilibrium equations in the form of complementarity conditions often appear as constraints in optimization problems. Problems of this type are commonly referred to as mathematical programs with complementarity constr...
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Equilibrium equations in the form of complementarity conditions often appear as constraints in optimization problems. Problems of this type are commonly referred to as mathematical programs with complementarity constraints (MPCCs). A popular method for solving MPCCs is the penalty interior-point algorithm (PIPA). This paper presents an example for which PIPA converges to a nonstationary point, providing a counterexample to the established theory. The reasons for this adverse behavior are discussed.
The problem of positioning p points so as to maximize the minimum distance between them has been studied in both location theory (as the continuous p-dispersion problem) and the design of computer experiments (as the ...
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The problem of positioning p points so as to maximize the minimum distance between them has been studied in both location theory (as the continuous p-dispersion problem) and the design of computer experiments (as the maximin distance design problem). This problem can be formulated as a nonlinear program, either exactly or approximately. We consider formulations of both types and demonstrate that, as p increases, it becomes dramatically more expensive to compute solutions of the exact formulation than to compute solutions of the approximate formulation.
This paper presents a new sequential method for constrained nonlinear optimization problems. The principal characteristics of these problems are very time consuming function evaluations and the absence of derivative i...
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This paper presents a new sequential method for constrained nonlinear optimization problems. The principal characteristics of these problems are very time consuming function evaluations and the absence of derivative information. Such problems are common in design optimization, where time consuming function evaluations are carried out by simulation tools (e.g., FEM, CFD). Classical optimization methods, based on derivatives, are not applicable because often derivative information is not available and is too expensive to approximate through finite differencing. The algorithm first creates an experimental design. In the design points the underlying functions are evaluated. Local linear approximations of the real model are obtained with help of weighted regression techniques. The approximating model is then optimized within a trust region to find the best feasible objective improving point. This trust region moves along the most promising direction, which is determined on the basis of the evaluated objective values and constraint violations combined in a filter criterion. If the geometry of the points that determine the local approximations becomes bad, i.e. the points are located in such a way that they result in a bad approximation of the actual model, then we evaluate a geometry improving instead of an objective improving point. In each iteration a new local linear approximation is built, and either a new point is evaluated (objective or geometry improving) or the trust region is decreased. Convergence of the algorithm is guided by the size of this trust region. The focus of the approach is on getting good solutions with a limited number of function evaluations. (C) 2003 Elsevier B.V. All rights reserved.
In this paper we discuss the application of optimization techniques for the design of several parts of the color picture tube, the key component of television sets and computer monitors. These projects have been carri...
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In this paper we discuss the application of optimization techniques for the design of several parts of the color picture tube, the key component of television sets and computer monitors. These projects have been carried out for Philips Display Components in Eindhoven. Philips developed several computer simulation models of picture tube parts. Designers use these models to simulate the physical behavior of a particular part design. Depending on the amount of detail in the model, the running time of a typical simulation ranges from one up to 10 hours. Tube designers are confronted with the problem of finding settings for a large number of design parameters that are optimal with respect to several simulated tube characteristics. This problem can be modeled as a so-called high-cost nonlinear programming problem. This paper reports on the successful application of our four-step compact model approach to solve this problem. The presented results are based on four projects in which we optimized picture tube parts. Among the realized benefits for Philips are a design improvement of 30% and a time-to-market reduction of 50-60%. (C) 2002 Elsevier Science B.V. All rights reserved.
An optimising design method is presented for designing closed grinding circuits to meet the requirements for the particulate product expressed as a combination of the mean value and standard deviation of the particle ...
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An optimising design method is presented for designing closed grinding circuits to meet the requirements for the particulate product expressed as a combination of the mean value and standard deviation of the particle size. The grinding circuit is modelled by a discrete mathematical model describing the axial mixing and breakage of particles in the mill and a possible time delay in the recycle line. The design problem is formulated as a nonlinear programming task in which the convective flow velocity and the axial dispersion coefficient of the ground material are selected as design variables. The method proved to be a useful tool for optimising design of grinding systems, and can be applied as a decision aid for process engineers to improve the efficiency of processes and maintaining the quality required for the particular products. (C) 2004 Elsevier B.V. All rights reserved.
Equilibrium equations in the form of complementarity conditions often appear as constraints in optimization problems. Problems of this type are commonly referred to as mathematical programs with complementarity constr...
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Equilibrium equations in the form of complementarity conditions often appear as constraints in optimization problems. Problems of this type are commonly referred to as mathematical programs with complementarity constraints (MPCCs). A popular method for solving MPCCs is the penalty interior-point algorithm (PIPA). This paper presents an example for which PIPA converges to a nonstationary point, providing a counterexample to the established theory. The reasons for this adverse behavior are discussed.
This paper provides an introductory survey of a class of optimization problems known as bilevel programming. We motivate this class through a simple application, and then proceed with the general formulation of bileve...
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This paper presents a game-theoretic method for analyzing the security of computer networks. We view the interactions between an attacker and the administrator as a two-player stochastic game and construct a model for...
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We describe four approaches to solving nonconvex global optimization problems by convex nonlinear programming methods. It is assumed that the problem becomes convex when selected variables are fixed. The selected vari...
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ISBN:
(纸本)354026003X
We describe four approaches to solving nonconvex global optimization problems by convex nonlinear programming methods. It is assumed that the problem becomes convex when selected variables are fixed. The selected variables must be discrete, or else discretized if they are continuous. We first survey some existing methods: disjunctive programming with convex relaxations, logic-based outer approximation, and logic-based Benders decomposition. We then introduce a branch-and-bound method with convex quasi-relaxations (BBCQ) that can be effective when the discrete variables take a large number of real values. The BBCQ method generalizes work of Bollapragada, Ghattas and Hooker on structural design problems. It applies when the constraint functions are concave in the discrete variables and have a weak homogeneity property in the continuous variables.
This paper relates the experience of use of the optimal power flow software IPSO (Integrated Power System Optimizer) for solving problems related to the Belgian power system short term operation and planning. The opti...
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ISBN:
(纸本)0780391918
This paper relates the experience of use of the optimal power flow software IPSO (Integrated Power System Optimizer) for solving problems related to the Belgian power system short term operation and planning. The optimization is performed using the KNITRO solver based on an interior point algorithm. After a short description of the main algorithm features, the paper focuses on the utilisation of OPF program to solve two main optimization problems typical of the operation of the Belgian grid system that is highly interconnected to the UCTE grid: a/ the evaluation of the steady state TTC (Total Transfer Capability) which is a key component of the ATC (Available transfer capability) provided to the market operators and the quantification of the TRM (Transfer Reliability Margin) b/ the supervision of the Tertiary Voltage Control (TVC) that implements the maximization of the units individual reactive power margin through the emulation of the highly customized linear programming algorithm implemented within the EMS software for operational or planning purposes.
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