On the implicit programming approach in a class of mathematical programs with equilibrium constraints
Jiří Outrata, Michal Červinka (2009)
Control and Cybernetics
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On the implicit programming approach in a class of mathematical programs with equilibrium constraints
A second order -approximation method for constrained optimization problems involving second order invex functions
Tadeusz Antczak (2009)
Applications of Mathematics
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A new approach for obtaining the second order sufficient conditions for nonlinear mathematical programming problems which makes use of second order derivative is presented. In the so-called second order -approximation method, an optimization problem associated with the original nonlinear programming problem is constructed that involves a second order -approximation of both the objective function and the constraint function constituting the original problem. The equivalence between...
A comparative study on optimization methods for the constrained nonlinear programming problems.
Yeniay, Ozgur (2005)
Mathematical Problems in Engineering
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Saddle points criteria via a second order -approximation approach for nonlinear mathematical programming involving second order invex functions
Tadeusz Antczak (2011)
Kybernetika
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In this paper, by using the second order -approximation method introduced by Antczak [3], new saddle point results are obtained for a nonlinear mathematical programming problem involving second order invex functions with respect to the same function . Moreover, a second order -saddle point and a second order -Lagrange function are defined for the so-called second order -approximated optimization problem constructed in this method. Then, the equivalence between an optimal solution...
Nonsmooth equation method for nonlinear nonconvex optimization
Lukšan, Ladislav, Matonoha, Ctirad, Vlček, Jan
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The contribution deals with the description of two nonsmooth equation methods for inequality constrained mathematical programming problems. Three algorithms are presented and their efficiency is demonstrated by numerical experiments.