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.
We present a class of trust region algorithms that do not use any penalty function or a filter for nonlinear equality constrained optimization. In each iteration, the infeasibility is controlled by a progressively dec...
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We present a class of trust region algorithms that do not use any penalty function or a filter for nonlinear equality constrained optimization. In each iteration, the infeasibility is controlled by a progressively decreasing upper limit and trial steps are computed by a Byrd-Omojokun-type trust region strategy. Measures of optimality and infeasibility are computed, whose relationship serves as a criterion on which the algorithm decides which one to focus on improving. As a result, the algorithm keeps a balance between the improvements on optimality and feasibility even if no restoration phase which is required by filter methods is used. The framework of the algorithm ensures the global convergence without assuming regularity or boundedness on the iterative sequence. By using a second order correction strategy, Marato's effect is avoided and fast local convergence is shown. The preliminary numerical results are reported. (C) 2012 Elsevier Ltd. All rights reserved.
A second-order dual to a nonlinear programming problem is formulated. This dual uses the Fritz John necessary optimality conditions instead of the Karush-Kuhn-Tucker necessary optimality conditions, and thus, does not...
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A second-order dual to a nonlinear programming problem is formulated. This dual uses the Fritz John necessary optimality conditions instead of the Karush-Kuhn-Tucker necessary optimality conditions, and thus, does not require a constraint qualification. Weak, strong, strict-converse, and converse duality theorems between primal and dual problems are established. (C) 2001 Elsevier Science Ltd. All rights reserved.
In this paper we consider inequality constrained nonlinear optimization problems where the first order derivatives of the objective function and the constraints cannot be used. Our starting point is the possibility to...
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In this paper we consider inequality constrained nonlinear optimization problems where the first order derivatives of the objective function and the constraints cannot be used. Our starting point is the possibility to transform the original constrained problem into an unconstrained or linearly constrained minimization of a nonsmooth exact penalty function. This approach shows two main difficulties: the first one is the nonsmoothness of this class of exact penalty functions which may cause derivative-free codes to converge to nonstationary points of the problem;the second one is the fact that the equivalence between stationary points of the constrained problem and those of the exact penalty function can only be stated when the penalty parameter is smaller than a threshold value which is not known a priori. In this paper we propose a derivative-free algorithm which overcomes the preceding difficulties and produces a sequence of points that admits a subsequence converging to a Karush-Kuhn-Tucker point of the constrained problem. In particular the proposed algorithm is based on a smoothing of the nondifferentiable exact penalty function and includes an updating rule which, after at most a finite number of updates, is able to determine a "right value" for the penalty parameter. Furthermore we present the results obtained on a real world problem concerning the estimation of parameters in an insulin-glucose model of the human body.
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.
This paper deals with multiobjective nonlinear programming problems with fuzzy parameters in the objective functions. These fuzzy parameters are characterized by fuzzy numbers. The existing results concerning the qual...
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This paper deals with multiobjective nonlinear programming problems with fuzzy parameters in the objective functions. These fuzzy parameters are characterized by fuzzy numbers. The existing results concerning the qualitative analysis of some basic notions in parametric nonlinear programming problems are reformulated to study the stability of multiobjective nonlinear programming problems under the concept of alpha-pareto optimality. An algorithm for obtaining any subset of the parametric space which has the same corresponding alpha-pareto optimal solution is also presented. An illustrative example is given to clarify the obtained results.
We define a primal-dual algorithm model (second-order Lagrangian algorithm, SOLA) for inequality constiained optimization problems that generates a sequence converging to points satisfying the second-order necessary c...
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We define a primal-dual algorithm model (second-order Lagrangian algorithm, SOLA) for inequality constiained optimization problems that generates a sequence converging to points satisfying the second-order necessary conditions for optimality. This property can be enforced by combining the equivalence between the original constrained problem and the unconstrained minimization of an exact augmented Lagrangian function and the use of a curvilinear line search technique that exploits information on the nonconvexity of the augmented Lagrangian function.
Two recently proposed algorithms for the problem of minimization subject to nonlinear equality constraints are examined. Both maintain quasi-Newton approximations to the projection of the Hessian of the Lagrangian, on...
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Two recently proposed algorithms for the problem of minimization subject to nonlinear equality constraints are examined. Both maintain quasi-Newton approximations to the projection of the Hessian of the Lagrangian, onto the (linearized) manifold of active constraints at each iteration. We show that both algorithms can be used with a more general quasi-Newton updating rule, and, using the analysis of Stoer (1984), that the sequence of projected Hessian approximations is convergent.
A computerized mathematical procedure based on nonlinear programming is presented for the purpose of a sandy soil parameter prediction problem by inverse analysis. The task of inverse analysis is to evaluate the value...
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A computerized mathematical procedure based on nonlinear programming is presented for the purpose of a sandy soil parameter prediction problem by inverse analysis. The task of inverse analysis is to evaluate the values of input parameters for a specified output or response of the system. This inverse problem to determine the values of system input parameters is mathematically formulated as a constrained optimization problem in this study. The input parameters are considered as design variables. The constraint set is developed through the implementation of lower and upper bound on design variables. The objective function is determined by evaluating the error or mismatch between the specified output (reference value) and the model predicted value for a given design vector. The resulting nonlinear programming problem is solved using the Interior Penalty Function method coupled with the Davidon-Fletcher-Powell method and quadratic interpolation scheme. To demonstrate the proposed methodology, two illustrative examples related to axially loaded piles installed in sandy soil medium are considered. The numerical results indicate that the back analyzed values are in good agreement with their respective reference values.
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