Displaying similar documents to “Convergence of primal-dual solutions for the nonconvex log-barrier method without LICQ”

Optimality conditions for a class of mathematical programs with equilibrium constraints: strongly regular case

Jiří V. Outrata (1999)

Kybernetika

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The paper deals with mathematical programs, where parameter-dependent nonlinear complementarity problems arise as side constraints. Using the generalized differential calculus for nonsmooth and set-valued mappings due to B. Mordukhovich, we compute the so-called coderivative of the map assigning the parameter the (set of) solutions to the respective complementarity problem. This enables, in particular, to derive useful 1st-order necessary optimality conditions, provided the complementarity...

First- and second-order optimality conditions for mathematical programs with vanishing constraints

Tim Hoheisel, Christian Kanzow (2007)

Applications of Mathematics

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We consider a special class of optimization problems that we call Mathematical Programs with Vanishing Constraints, MPVC for short, which serves as a unified framework for several applications in structural and topology optimization. Since an MPVC most often violates stronger standard constraint qualification, first-order necessary optimality conditions, weaker than the standard KKT-conditions, were recently investigated in depth. This paper enlarges the set of optimality criteria...

Sufficient Second Order Optimality Conditions for C^1 Multiobjective Optimization Problems

Gadhi, N. (2003)

Serdica Mathematical Journal

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2000 Mathematics Subject Classification: Primary 90C29; Secondary 90C30. In this work, we use the notion of Approximate Hessian introduced by Jeyakumar and Luc [19], and a special scalarization to establish sufficient optimality conditions for constrained multiobjective optimization problems. Throughout this paper, the data are assumed to be of class C^1, but not necessarily of class C^(1.1).

Nonlinear Rescaling Method and Self-concordant Functions

Richard Andrášik (2013)

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

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Nonlinear rescaling is a tool for solving large-scale nonlinear programming problems. The primal-dual nonlinear rescaling method was used to solve two quadratic programming problems with quadratic constraints. Based on the performance of primal-dual nonlinear rescaling method on testing problems, the conclusions about setting up the parameters are made. Next, the connection between nonlinear rescaling methods and self-concordant functions is discussed and modified logarithmic barrier...