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Decomposition Method for nonlinear programming problems of Chemical Processes

KAGAKU KOGAKU RONBUNSHU 2010年第5期36卷 512-518页

作者： Wakahara, Tatsuro Noda, Masaru Nishitani, Hirokazu Nara Inst Sci & Technol Grad Sch Informat Sci Ikoma Nara 6300192 Japan

Optimization problems of chemical process can generally be formulated as nonlinear programming problems, but the objective functions and the constraints of problems are often linear for most variables. In this paper, we propose a new decomposition method for nonlinear programming problems with two types of variables;linear and nonlinear variables. The proposed method is more effective than a nonlinear optimization method without decomposition to solve problems containing a relatively small number of nonlinear variables, because the dimension of the decomposed problem is much smaller than that of the original problem. Some computational results for the Rosen-Suzuki test problem indicate that the proposed method is useful for reducing the computational time.

关键词： Chemical Process Optimization nonlinear programming problem Decomposition Method Rosen-Suzuki Test problem

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OPTIMALITY CONDITIONS VIA EXACT PENALTY FUNCTIONS

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SIAM JOURNAL ON OPTIMIZATION 2010年第6期20卷 3208-3231页

作者： Meng, K. W. Yang, X. Q. Hong Kong Polytech Univ Dept Appl Math Kowloon Hong Kong Peoples R China

In this paper, we study KKT optimality conditions for constrained nonlinear programming problems and strong and Mordukhovich stationarities for mathematical programs with complementarity constraints using l(p) penalty functions, with 0 <= p <= 1. We introduce some optimality indication sets by using contingent derivatives of penalty function terms. Some characterizations of optimality indication sets are obtained by virtue of the original problem data. We show that the KKT optimality condition holds at a feasible point if this point is a local minimizer of some l(p) penalty function with p belonging to the optimality indication set. Our result on constrained nonlinear programming includes some existing results from the literature as special cases.

关键词： KKT optimality condition nonlinear programming problem mathematical programs with complementarity constraints strong stationarity Mordukhovich stationarity exact penalty function

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Solutions for fuzzy matrix games

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COMPUTERS & MATHEMATICS WITH APPLICATIONS 2010年第3期60卷 399-410页

作者： Cevikel, Adem C. Ahlatcioglu, Mehmet Yildiz Tekn Univ Art & Sci Fac Dept Math Istanbul Turkey

In this paper, we deal with two-person zero-sum games with fuzzy payoffs and fuzzy goals. We have presented two models for studying two-person zero-sum matrix games with fuzzy payoffs and fuzzy goals. We assume that each player has a fuzzy goal for each of the payoffs. We obtained that the fuzzy relation approach and the max-min solution are equivalent. (C) 2010 Elsevier Ltd. All rights reserved.

关键词： Fuzzy goal Fuzzy payoff matrix Fuzzy relation Fuzzy quantity nonlinear programming problem Max-min solution Relaxation procedure Two-person zero-sum games

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Design of Bridge Transport System with Equal Incremental Telescopic Motion

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TRANSACTIONS OF THE KOREAN SOCIETY OF MECHANICAL ENGINEERS A 2010年第2期34卷 227-235页

作者： Yoon, Kwang Ho Lee, Hyo Jik Lee, Jong Kwang Park, Byung Suk Kim, Kiho Korea Inst Machinery & Mat Daejeon South Korea Korea Atom Energy Res Inst Daejeon South Korea

This paper introduces the design of a bridge transport system with a telescopic tube for positioning equipment to perform remote handling tasks in a radioactive facility. It consists of an extensible and retractable telescopic tube assembly for z-direction motion, a cabling system for management of power and signal cables, and a trolley system for transverse motion and accommodating servo drives. The working environment for the bridge transport system with the telescopic tube requires strict geometrical constraints, including a short height, short telescopic tube length when retracted, and a long stroke. These constraints were met by solving a nonlinear programming problem involving the optimal dimensions. This paper introduces a cabling system for effective management of cables with changeable lengths to accommodate telescopic motions and a selection guide for servo drives that are sufficient to drive the system.

关键词： Bridge Transport System Telescopic Tube PRIDE nonlinear programming problem BDSM

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Optimal control problems involving constrained, switched, and delay systems

Optimal control problems involving constrained, switched, an...

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作者： Loxton, Ryan Christopher Curtin University of Technology

学位级别：master

In this thesis, we develop numerical methods for solving five nonstandard optimal control problems. The main idea of each method is to reformulate the optimal control problem as, or approximate it by, a nonlinear programming problem. The decision variables in this nonlinear programming problem influence its cost function (and constraints, if it has any) implicitly through the dynamic system. Hence, deriving the gradient of the cost and the constraint functions is a difficult task. A major focus of this thesis is on developing methods for computing these gradients. These methods can then be used in conjunction with a gradient-based optimization technique to solve the optimal control problem efficiently.%%%%The first optimal control problem that we consider has nonlinear inequality constraints that depend on the state at two or more discrete time points. These time points are decision variables that, together with a control function, should be chosen in an optimal manner. To tackle this problem, we first approximate the control by a piecewise constant function whose values and switching times (the times at which it changes value) are decision variables. We then apply a novel time-scaling transformation that maps the switching times to fixed points in a new time horizon. This yields an approximate dynamic optimization problem with a finite number of decision variables. We develop a new algorithm, which involves integrating an auxiliary dynamic system forward in time, for computing the gradient of the cost and constraints in this approximate problem.%%%%The second optimal control problem that we consider has nonlinear continuous inequality constraints. These constraints restrict both the state and the control at every point in the time horizon. As with the first problem, we approximate the control by a piecewise constant function and then transform the time variable. This yields an approximate semi-infinite programming problem, which can be solved using a penalty functi

关键词： optimal control problems numerical methods nonlinear programming problem decision variables cost functions dynamic system constraint functions gradient-based optimization technique

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An improved Genetic Algorithm for a Type of nonlinear programming problems

An improved Genetic Algorithm for a Type of Nonlinear Progra...

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IEEE International Conference on Automation and Logistics

作者： He Dakuo Wang Fuli Jia Mingxing Minist Educ Key Lab Proc Ind Automat Shenyang 110004 Peoples R China

ISBN: (纸本)9781424425020

Based on the study on how to apply penalty strategy for solving a type of nonlinear programming problems by genetic algorithm, such conclusion can be drawn that only applying penalty strategy is inadequate to deal with nonlinear programming problems well. It is important to lead infeasible individuals into the feasible set during the evolution process. Penalty and repair strategy are associated to improve the performance of the algorithm. Based on such thought that the constraint which has the highest degree of violation can be satisfied first by enlarging the penalty on the individuals and repair, repair operator is proposed to perform repair operation of infeasible individuals. At the same time, based on optimization design theory, a method has been proposed to establish initial population by using uniform design. Thus, repair genetic algorithm (RGA) is proposed.

关键词： nonlinear programming problem genetic algorithm uniform design penalty strategy repair strategy repair operator

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Direct optimization of dynamic systems described by differential-algebraic equations

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OPTIMAL CONTROL APPLICATIONS & METHODS 2008年第6期29卷 445-466页

作者： Fabien, Brian C. Univ Washington Dept Mech Engn Seattle WA 98195 USA

This paper presents a method for the optimization of dynamic systems described by index-1 differential-algebraic equations (DAE). The class of problems addressed include optimal control problems and parameter identification problems. Here, the controls are parameterized using piecewise constant inputs on a grid in the time interval of interest. In addition, the DAE are approximated using a Rosenbrock-Wanner (ROW) method. In this way the infinite-dimensional optimal control problem is transformed into a finite-dimensional nonlinear programming problem (NLP). The NLP is solved using a sequential quadratic programming (QP) technique that minimizes the L,,, exact penalty function, using only strictly convex QP subproblems. This paper shows that the ROW method discretization of the DAE leads to (i) a relatively small NLP problem and (ii) an efficient technique for evaluating the function, constraints and gradients associated with the NLP problem. This paper also investigates a state mesh refinement technique that ensures a sufficiently accurate representation of the optimal state trajectory. Two nontrivial examples are used to illustrate the effectiveness of the proposed method. Copyright (C) 2008 John Wiley & Sons, Ltd.

关键词： nonlinear optimal control parameter identification nonlinear programming problem Rosenbrock-Wanner method

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Implementation of a robust SQP algorithm

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OPTIMIZATION METHODS & SOFTWARE 2008年第6期23卷 827-846页

作者： Fabien, Brian C. Univ Washington Dept Mech Engn Seattle WA 98195 USA

This paper presents an implementation of a sequential quadratic programming (SQP) algorithm for the solution of nonlinear programming (NLP) problems. In the proposed algorithm, a solution to the NLP problem is found by minimizing the L1 exact penalty function. The search direction for the penalty function minimization is determined by solving a strictly convex quadratic programming (QP) problem. Here, we make the basic SQP algorithm more robust (i) by solving a relaxed, strictly convex, QP problem in cases where the constraints are inconsistent, (ii) by performing a non-monotone line search to improve efficiency, and (iii) by using second-order corrections to avoid the Maratos effect. The robustness of the algorithm is demonstrated via a C language implementation that is applied to numerous parameter optimization and optimal control problems that have appeared in the literature. The results obtained show that both non-monotone line searches and second-order corrections can significantly reduce the amount of work required to solve parameter optimization problems.

关键词： nonlinear programming problem sequential quadratic programming computer code

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Parameter optimization using the L_∞ exact penalty function and strictly convex quadratic programming problems

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APPLIED MATHEMATICS AND COMPUTATION 2008年第2期198卷 833-848页

作者： Fabien, Brian C. Univ Washington Dept Mech Engn Seattle WA 98195 USA

This paper presents an algorithm for the numerical solution of constrained parameter optimization problems. The solution strategy is based on a sequential quadratic programming (SQP) technique that uses the L-infinity exact penalty function. Unlike similar SQP algorithms the method proposed here solves only strictly convex quadratic programs to obtain the search directions. The global convergence properties of the algorithm are enhanced by the use of a nonmonotone line search and second-order corrections to avoid the Maratos effect. The paper also presents an ANSI C implementation of the algorithm. The effectiveness of the proposed method is demonstrated by solving numerous parameter optimization and optimal control problems that have appeared in the literature. (C) 2007 Elsevier Inc. All rights reserved.

关键词： nonlinear programming problem sequential quadratic programming convex quadratic programming computer code

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Particle swarm optimization based heuristics for nonlinear programming problems

Particle swarm optimization based heuristics for nonlinear p...

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International Multiconference of Engineers and Computer Scientists

作者： Matsui, Takeshi Kato, Kosuke Sakawa, Masatoshi Uno, Takeshi Morihara, Kenji Hiroshima Univ Grad Sch Engn Hiroshima Japan

ISBN: (纸本)9789889867140

In recent years, a high speed and accurate optimization method has been expected for large scale nonlinear programming problems. As a new solution method for nonlinear programming problems, a particle swarm optimization (PSO) method was proposed by Kennedy et al. and has attracted considerable attention. However, there exist few reports with respect to successful results for constrained nonlinear programming problems by PSO-based methods. Furthermore, PSO-based methods have a shortcoming that the search is liable to stopping at a certain local solution. In this paper, incorporating the bisection method and a homomorphous mapping to carry out the search considering constraints as well as the multiple stretching technique and modified move schemes of particles to restraining the stopping around local solutions. Furthermore, we show the efficiency of the proposed revised PSO method (rPSO) by comparing it with an existing method through the application of them into the numerical examples.

关键词： nonlinear programming problem particle swarm optimization bisection method homomorphous mapping multiple stretching

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