The aim of this paper is to study a nondifferentiable minimax programming problem with square root terms in the objective functions and establish sufficient optimality conditions from the standpoint of the higher-orde...
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We present here a characterization of the Clarke subdifferential of the optimal value function of a linear program as a function of matrix coefficients. We generalize the result of Freund (1985) to the cases where der...
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We present here a characterization of the Clarke subdifferential of the optimal value function of a linear program as a function of matrix coefficients. We generalize the result of Freund (1985) to the cases where derivatives may not be defined because of the existence of multiple primal or dual solutions. (c) 2020 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://***/licenses/by-nc-nd/4.0/)
In this paper, we present new class of higher-order (C, alpha, rho, d)-convexity and formulate two types of higher-order duality for a nondifferentiable minimax fractional programming problem. Based on the higher-orde...
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In this paper, we present new class of higher-order (C, alpha, rho, d)-convexity and formulate two types of higher-order duality for a nondifferentiable minimax fractional programming problem. Based on the higher-order (C, alpha, rho, d)-convexity, we establish appropriate higher-order duality results. These results extend several known results to a wider class of programs.
In this paper, we have pointed out that the proofs of the Theorems 3.1 and 3.3 in the recent paper (Sonali et al. in Ann Oper Res 244:603-617, 2016) are erroneous. A modified dual to the second order minimax fractiona...
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In this paper, we have pointed out that the proofs of the Theorems 3.1 and 3.3 in the recent paper (Sonali et al. in Ann Oper Res 244:603-617, 2016) are erroneous. A modified dual to the second order minimax fractional programming problem has been formulated and the rectified proofs of these results under generalized B-(p,r)-invexity have been established.
The advantage of second-order duality is that if a feasible point of the primal is given and first-order duality conditions are not applicable (infeasible), then we may use second-order duality to provide a lower boun...
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The advantage of second-order duality is that if a feasible point of the primal is given and first-order duality conditions are not applicable (infeasible), then we may use second-order duality to provide a lower bound for the value of primal problem. Consequently, it is quite interesting to discuss the duality results for the case of second order. Thus, we focus our study on a discussion of duality relationships of a minimax fractional programming problem under the assumptions of second order B-(p, r)-invexity. Weak, strong and strict converse duality theorems are established in order to relate the primal and dual problems under the assumptions. An example of a non trivial function has been given to show the existence of second order B-(p, r)-invex functions.
Two types of second-order dual models for a nondifferentiable minimax fractional programming problem are formulated and proved weak, strong, strict converse duality theorems using ri-bonvexity assumptions. Special cas...
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Two types of second-order dual models for a nondifferentiable minimax fractional programming problem are formulated and proved weak, strong, strict converse duality theorems using ri-bonvexity assumptions. Special cases are also discussed to show that this work extends some known results of the literature. (C) 2013 Elsevier B.V. All rights reserved.
In this paper, we derive appropriate duality theorems for three second-order dual models of a nondifferentiable minimax fractional programming problem under second-order (C, alpha, rho, d)-convexity assumptions. A non...
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In this paper, we derive appropriate duality theorems for three second-order dual models of a nondifferentiable minimax fractional programming problem under second-order (C, alpha, rho, d)-convexity assumptions. A nontrivial example has also been exemplified to show the existence of second-order (C, alpha, rho, d)-convex functions. Several known results including many recent works are obtained as special cases.
The Multisource Weber problem, also known as the continuous location-allocation problem, or as the Fermat-Weber problem, is considered here. A particular case of the Multisource Weber problem is the minimum sum-of-dis...
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The Multisource Weber problem, also known as the continuous location-allocation problem, or as the Fermat-Weber problem, is considered here. A particular case of the Multisource Weber problem is the minimum sum-of-distances clustering problem, also known as the continuous -median problem. The mathematical modelling of this problem leads to a formulation which, in addition to its intrinsic bi-level nature, is strongly nondifferentiable. Moreover, it has a large number of local minimizers, so it is a typical global optimization problem. In order to overcome the intrinsic difficulties of the problem, the so called Hyperbolic Smoothing methodology, which follows a smoothing strategy using a special differentiable class function, is adopted. The final solution is obtained by solving a sequence of low dimension differentiable unconstrained optimization sub-problems which gradually approaches the original problem. For the purpose of illustrating both the reliability and the efficiency of the method, a set of computational experiments making use of traditional test problems described in the literature was performed. Apart from consistently presenting better results when compared to related approaches, the novel technique introduced here was able to deal with instances never tackled before in the context of the Multisource Weber problem.
The Multisource Weber problem, also known as the continuous location-allocation problem, or as the Fermat-Weber problem, is considered here. A particular case of the Multisource Weber problem is the minimum sum-of-dis...
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The Multisource Weber problem, also known as the continuous location-allocation problem, or as the Fermat-Weber problem, is considered here. A particular case of the Multisource Weber problem is the minimum sum-of-distances clustering problem, also known as the continuous -median problem. The mathematical modelling of this problem leads to a formulation which, in addition to its intrinsic bi-level nature, is strongly nondifferentiable. Moreover, it has a large number of local minimizers, so it is a typical global optimization problem. In order to overcome the intrinsic difficulties of the problem, the so called Hyperbolic Smoothing methodology, which follows a smoothing strategy using a special differentiable class function, is adopted. The final solution is obtained by solving a sequence of low dimension differentiable unconstrained optimization sub-problems which gradually approaches the original problem. For the purpose of illustrating both the reliability and the efficiency of the method, a set of computational experiments making use of traditional test problems described in the literature was performed. Apart from consistently presenting better results when compared to related approaches, the novel technique introduced here was able to deal with instances never tackled before in the context of the Multisource Weber problem.
In this paper, we are concerned with a class of nondifferentiable minimax programming problem and its two types of second order dual models. Weak, strong and strict converse duality theorems from a view point of gener...
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In this paper, we are concerned with a class of nondifferentiable minimax programming problem and its two types of second order dual models. Weak, strong and strict converse duality theorems from a view point of generalized convexity are established. Our study naturally unifies and extends some previously known results on minimax programming.
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