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.
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.
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.
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.
An important challenge for most chemical companies is, to simultaneously consider inventory optimization and supply chain network design under demand uncertainty. This leads to a problem that requires integrating a st...
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An important challenge for most chemical companies is, to simultaneously consider inventory optimization and supply chain network design under demand uncertainty. This leads to a problem that requires integrating a stochastic inventory model with the supply chain network design model. This problem can be formulated as a large-scale combinatorial optimization model that includes nonlinear terms. Since these models are very difficult to solve. they require exploiting their properties and developing special solution techniques to reduce the computational effort. In this work, we analyze the properties of the basic model and develop solution techniques for a joint Supply chain network design and inventory management model for a given product. The model is formulated as a nonlinear integer programming problem. By reformulating it as a mixed-integer nonlinear programming (MINLP) problem and using an associated convex relaxation model for initialization. we first propose a heuristic method to quickly obtain good-quality solutions. Further. a decomposition algorithm based on Lagrangean relaxation is developed for obtaining global or near-global optimal solutions. Extensive computational examples with up to 150 distribution centers and 150 retailers are presented to illustrate the performance of the algorithms and to compare them with the full-space solution.
Water allocation under limited water supplies is becoming more important as water becomes scarcer. Optimization models are frequently used to provide decision support to enhance water allocation under limited water su...
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Water allocation under limited water supplies is becoming more important as water becomes scarcer. Optimization models are frequently used to provide decision support to enhance water allocation under limited water supplies. Correct modelling of the underlying soil-moisture balance calculations at the field scale, which governs optimal allocation of water is a necessity for decision-making. Research shows that the mathematical programming formulation of soil-moisture balance calculations presented by Ghahraman and Sepaskhah (2004) may malfunction under limited water supplies. A new model formulation is presented in this research that explicitly models deep percolation and evapotranspiration as a function of soil-moisture content. The new formulation also allows for the explicit modelling of inefficiencies resulting from nonuniform irrigation. Modelling inefficiencies are key to the evaluation of the economic profitability of deficit irrigation. Ignoring increasing efficiencies resulting from deficit irrigation may render deficit irrigation unprofitable. The results show that ignoring increasing efficiencies may overestimate the impact of deficit irrigation on maize yields by a maximum of 2.2 tons per hectare.
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