Within the context of sequential methods for solving general nonlinear programming problems, and on the grounds of a previous work of the same authors, this study deals with the theoretical reasoning behind handling t...
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Within the context of sequential methods for solving general nonlinear programming problems, and on the grounds of a previous work of the same authors, this study deals with the theoretical reasoning behind handling the original subproblems by an augmentation strategy. We do not assume feasibility of the original problem, nor the fulfillment of any constraint qualification. The previous analysis is extended along two directions. First and foremost, the exact nature of the stationary points previously considered is alleviated under an approximate stationary perspective. Second, the current analysis has been developed using general vector norms. Therefore, despite the similarities of the obtained results with those of the prior study, the present ones have been obtained under less restrictive hypotheses, and with a more involved examination. As before, we are not concerned with the sequential method itself, nor with computational results. We focus on the features of the original problem that can be inferred from the properties of the solution of the augmented problem, with the solutions being now analyzed in an approximate sense. Examples illustrating the obtained results are included.
This paper presents it combined genetic algorithm-fuzzy logic controller (GA-FLC) technique for constrained nonlinear programming problems. In the standard Genetic algorithms, the upper and lower limits of the search ...
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This paper presents it combined genetic algorithm-fuzzy logic controller (GA-FLC) technique for constrained nonlinear programming problems. In the standard Genetic algorithms, the upper and lower limits of the search regions Should be given by the decision maker in advance to the optimization process. In general it needlessly large search region is used in fear of missing the global Optimum Outside the search region. Therefore, if the search region is able to adapt toward a promising area during the optimization process, the performance of GA will be enhanced greatly. Thus in this work we tried to investigate the influence of the bounding intervals on the final result. The proposed algorithm is made of classical GA Coupled with FLC. This controller monitors the variation of the decision variables during process of the algorithm and modifies the boundary intervals to restart the next round of the algorithm. These characteristics make this approach well suited for finding optimal solutions to the highly NLP problems. Compared to previous works on NLP, our method proved to be more efficient in Computation time and accuracy of the final solution. (c) 2005 Elsevier Inc. All rights reserved.
An inexact restoration derivative-free filter method for nonlinear programming is introduced in this paper. Each iteration is composed of a restoration phase, which reduces a measure of infeasibility, and an optimizat...
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An inexact restoration derivative-free filter method for nonlinear programming is introduced in this paper. Each iteration is composed of a restoration phase, which reduces a measure of infeasibility, and an optimization phase, which reduces the objective function. The restoration phase is solved using a derivative-free method for solving underdetermined nonlinear systems with bound constraints, developed previously by the authors. An alternative for solving the optimization phase is considered. Theoretical convergence results and some preliminary numerical experiments are presented.
This paper illustrates how nonlinear programming and simulation tools, which are available in packages such as MATLAB and SIMULINK, can easily be used to solve optimal control problems with state- and/or input-depende...
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This paper illustrates how nonlinear programming and simulation tools, which are available in packages such as MATLAB and SIMULINK, can easily be used to solve optimal control problems with state- and/or input-dependent inequality constraints. The method presented is illustrated with a model of a single-link manipulator. The method is suitable to be taught to advanced undergraduate and Master's level students in control engineering.
A new approach is described for reducing the number of the fitness and constraint function evaluations required by a genetic algorithm (GA) for optimization problems with mixed continuous and discrete design variables...
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A new approach is described for reducing the number of the fitness and constraint function evaluations required by a genetic algorithm (GA) for optimization problems with mixed continuous and discrete design variables. The proposed additions to the GA make the search more effective and rapidly improve the fitness value from generation to generation. The additions involve memory as a function of both discrete and continuous design variables and multivariate approximation of the individual functions' responses in terms of several continuous design variables.. W The, approximation is demonstrated for the minimum weight design of a composite cylindrical shell with grid stiffeners.
In this paper, a new set of necessary conditions for optimality is introduced with reference to the differentiable nonlinear programming problem. It is shown that these necessary conditions are sharper than the usual ...
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In this paper, a new set of necessary conditions for optimality is introduced with reference to the differentiable nonlinear programming problem. It is shown that these necessary conditions are sharper than the usual Fritz John ones. A constraint qualification relevant to the new necessary conditions is defined and extensions to the locally Lipschitz case are presented.
Recently, Gulati and Craven and Mond and Egudo established strict converse duality theorems for some of Mond-Weir duals for nonlinear programming problems. Here, we establish various duality theorems under weaker conv...
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Recently, Gulati and Craven and Mond and Egudo established strict converse duality theorems for some of Mond-Weir duals for nonlinear programming problems. Here, we establish various duality theorems under weaker convexity conditions that are different from those of Gulati and Craven, Mond and Weir, and Mond and Egudo.
We propose a system of differential equations to find a Kuhn-Tucker point of a nonlinear programming problem with both equality and inequality constraints. It is proven that the Kuhn-Tucker point of the nonlinear prog...
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We propose a system of differential equations to find a Kuhn-Tucker point of a nonlinear programming problem with both equality and inequality constraints. It is proven that the Kuhn-Tucker point of the nonlinear programming problem is an asymptotically stable equilibrium point of the proposed differential system. An iterate algorithm is constructed to find an equilibrium point of the differential system, the global convergence and local quadratic convergence rate of this algorithm are demonstrated, and illustrative examples are given. (c) 2006 Elsevier Inc. All rights reserved.
This paper describes a nonlinear programming-based robust design methodology for controllers and prefilters of a predefined structure for the linear time-invariant systems involved in the quantitative feedback theory....
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This paper describes a nonlinear programming-based robust design methodology for controllers and prefilters of a predefined structure for the linear time-invariant systems involved in the quantitative feedback theory. This controller and prefilter synthesis problem is formulated as a single optimization problem with a given performance optimization objective and constraints enforcing stability and various specifications usually enforced in the quantitative feedback theory. The focus is set on providing constraints expression that can be used in standard nonlinear programming solvers. The nonlinear solver then computes in a single-step controller and prefilter design parameters that satisfy the prescribed constraints and maximizes the performance optimization objective. The effectiveness of the proposed approach is demonstrated through a variety of difficult design cases like resonant plants, open-loop unstable plants, and plants with variation in the time delay. Copyright (c) 2016 John Wiley & Sons, Ltd.
This article introduces a methodology for designing the geometry of diffuse-walled radiant enclosures through nonlinear programming. In this application, the enclosure is represented parametrically using B-spline curv...
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This article introduces a methodology for designing the geometry of diffuse-walled radiant enclosures through nonlinear programming. In this application, the enclosure is represented parametrically using B-spline curves, while the radiosity distribution is solved by infinitesimal-area analysis. The enclosure geometry is repeatedly adjusted with a gradient-based minimization algorithm until a near-optimum solution is found This approach requires far less design time than the forward "trial-and-error" methodology, and the quality of the final solution is usually much better. The methodology is demonstrated by optimizing the geometry of a 2-D radiant enclosure, with the objective of obtaining a desired radiosity distribution over a portion of the enclosure surface.
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