In this paper, the optimization techniques for solving a class of non-differentiable optimization problems are investigated. The non-differentiable programming is transformed into an equivalent or approximating differ...
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In this paper, the optimization techniques for solving a class of non-differentiable optimization problems are investigated. The non-differentiable programming is transformed into an equivalent or approximating differentiableprogramming. Based on Karush-Kuhn-Tucker optimality conditions and projection method, a neural network model is constructed. The proposed neural network is proved to be globally stable in the sense of Lyapunov and can obtain an exact or approximating optimal solution of the original optimization problem. An example shows the effectiveness of the proposed optimization techniques. (C) 2009 Published by Elsevier Ltd
A pair of Wolfe type non-differentiable second order symmetric primal and dual problems in mathematical programming is formulated, The weak and strong duality theorems are then established under second order F-convexi...
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A pair of Wolfe type non-differentiable second order symmetric primal and dual problems in mathematical programming is formulated, The weak and strong duality theorems are then established under second order F-convexity assumptions, Symmetric minimax mixed integer primal and dual problems are also investigated. (C) 2002 Elsevier Science B.V. All rights reserved.
Two pairs of non-differentiable multiobjective symmetric dual problems with cone constraints over arbitrary cones, which are Wolfe type and Mond-Weir type, are considered. On the basis of weak efficiency with respect ...
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Two pairs of non-differentiable multiobjective symmetric dual problems with cone constraints over arbitrary cones, which are Wolfe type and Mond-Weir type, are considered. On the basis of weak efficiency with respect to a convex cone, we obtain symmetric duality results for the two pairs of problems under cone-invexity and cone-pseudoinvexity assumptions on the involved functions. Our results extend the results in Khurana [S. Khurana, Symmetric duality in multiobjective programming involving generalized cone-invex functions, European Journal of Operational Research 165 (2005) 592-597] to the non-differentiable multiobjective symmetric dual problem. (C) 2007 Elsevier B.V. All rights reserved.
A pair of non-differentiable higher-order symmetric dual model in mathematical programming is formulated. The weak and strong duality theorems are established under higher-order-invexity assumption, Symmetric minimax ...
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A pair of non-differentiable higher-order symmetric dual model in mathematical programming is formulated. The weak and strong duality theorems are established under higher-order-invexity assumption, Symmetric minimax mixed integer primal and dual problems are also investigated. (c) 2004 Elsevier B.V. All rights reserved.
A pair of Mond-Weir type non-differentiable second order symmetric minimax mixed integer primal and dual problems in mathematical programming is formulated. Symmetric and self-duality theorems are then established und...
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A pair of Mond-Weir type non-differentiable second order symmetric minimax mixed integer primal and dual problems in mathematical programming is formulated. Symmetric and self-duality theorems are then established under second order F-pseudo-convexity assumptions. Several known results including that of Gulati and Ahmad [Eur. J. Oper. Res. 101 (1997) 122], Hou and Yang [J. Math. Anal. Appl. 255 (2001) 491] and Mond and Schechter [Bull. Aust. Math. Soc. 53 (1996) 177], as well as others are obtained as special cases. (c) 2004 Elsevier B.V. All rights reserved.
We consider the problem of optimally covering plane domains by a given number of circles. The mathematical modeling of this problem leads to a min-max-min formulation which, in addition to its intrinsic multi-level na...
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We consider the problem of optimally covering plane domains by a given number of circles. The mathematical modeling of this problem leads to a min-max-min formulation which, in addition to its intrinsic multi-level nature, has the significant characteristic of being non-differentiable. In order to overcome these difficulties, we have developed a smoothing strategy using a special class C-infinity smoothing function. The final solution is obtained by solving a sequence of differentiable subproblems which gradually approach the original problem. The use of this technique, called Hyperbolic Smoothing, allows the main difficulties presented by the original problem to be overcome. A simplified algorithm containing only the essential of the method is presented. For the purpose of illustrating both the actual working and the potentialities of the method, a set of computational results is presented.
In the last years the O-D matrix adjustment problem using link counts on a traffic network modelled by means of a static user equilibrium approach has been formulated advantageously by means of bilevel programs. The a...
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In the last years the O-D matrix adjustment problem using link counts on a traffic network modelled by means of a static user equilibrium approach has been formulated advantageously by means of bilevel programs. The algorithms developed to solve the problem present heuristic components in a lesser or greater degree. In this paper two new algorithmic alternatives are presented for this problem. The first alternative is an hybrid scheme proximal point-steepest descent that is based on a development of Codina for the approximation of the steepest descent direction of the upper level function and the second alternative is developed by Garcia and Marin and consists of solving a sequence of simplified bilevel programs. In order to highlight the characteristics of the two methods a set of test problems have been solved in conjunction with other well known methods, such as the method of Spiess, the method of Chan, the method of Yang as well as with an adaptation of the Wolfe's conjugate directions method for non-differentiable optimization, in order to provide a better perspective of their advantages and tradeoffs. (c) 2005 Elsevier B.V. All rights reserved.
The control of pressure surges in a pipeline is an important problem in many areas of industry, including hydroelectric power generation, oil refineries and chemical processing plants. This paper deals with the contro...
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The control of pressure surges in a pipeline is an important problem in many areas of industry, including hydroelectric power generation, oil refineries and chemical processing plants. This paper deals with the control of pressure surges in a simple system consisting of a single horizontal pipe. The methodology, however, is easily extended to more complex systems and is quite easily implemented. The control problem is formulated as a nonlinear minimax optimization problem. Due to the large-scale nature of such problems, a successive linear programming (LP) method is adopted. The convergence of the method is accelerated by a conjugate gradient type search. Computational results are also provided.
A linear sharing problem is defined as a mathematical programming problem with a max-min objective function comprised of continuous, non-decreasing trade-off functions and linear constraints. In this paper several sha...
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A linear sharing problem is defined as a mathematical programming problem with a max-min objective function comprised of continuous, non-decreasing trade-off functions and linear constraints. In this paper several sharing models are proposed where the objective function involves ratios in various forms. For such ratio-sharing problems, some properties are derived, efficient algorithms are proposed, and computational experience is reported.
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