http://repub.eur.nl/res/aut/5617/ List of Publications en http://repub.eur.nl/static-eur/img/logo.png http://repub.eur.nl http://repub.eur.nl/res/pub/19255/ 2007-07-01T00:00:00Z In this note we give an elementary proof of the Fritz-John and Karush–Kuhn–Tucker conditions for nonlinear finite dimensional programming problems with equality and/or inequality constraints. The proof avoids the implicit function theorem usually applied when dealing with equality constraints and uses a generalization of Farkas lemma and the Bolzano-Weierstrass property for compact sets. http://repub.eur.nl/res/pub/19277/ 2006-03-16T00:00:00Z We consider equilibrium constrained optimization problems, which have a general formulation that encompasses well-known models such as mathematical programs with equilibrium constraints, bilevel programs, and generalized semi-infinite programming problems. Based on the celebrated KKM lemma, we prove the existence of feasible points for the equilibrium constraints. Moreover, we analyze the topological and analytical structure of the feasible set. Alternative formulations of an equilibrium constrained optimization problem (ECOP) that are suitable for numerical purposes are also given. As an important first step for developing efficient algorithms, we provide a genericity analysis for the feasible set of a particular ECOP, for which all the functions are assumed to be linear. http://repub.eur.nl/res/pub/7030/ 2005-11-07T00:00:00Z In this note we give an elementary proof of the Fritz-John and Karush-Kuhn-Tucker conditions for nonlinear finite dimensional programming problems with equality and/or inequality constraints.The proof avoids the implicit function theorem usually applied when dealing with equality constraints and uses a generalization of Farkas lemma and the Bolzano-Weierstrass property for compact sets. http://repub.eur.nl/res/pub/6992/ 2005-10-14T00:00:00Z In this note we give an elementary proof of the Fritz-John and Karush-Kuhn-Tucker conditions for nonlinear finite dimensional programming problems with equality and/or inequality constraints. The proof avoids the implicit function theorem usually applied when dealing with equality constraints and uses a generalization of Farkas lemma and the Bolzano-Weierstrass property for compact sets. http://repub.eur.nl/res/pub/1927/ 2005-04-01T00:00:00Z In this note we show that the strong duality theorem of an unconstrained (generalized) geometric programming problem as defined by Peterson (cf.[1]) is actually a special case of a Lagrangian duality result. Contrary to [1] we also consider the case that the set C is compact and convex and in this case we do not need to assume the standard regularity condition. http://repub.eur.nl/res/pub/19412/ 2005-04-01T00:00:00Z In this note we show that the strong duality theorem of an unconstrained (generalized) geometric programming problem as defined by Peterson (cf.[1]) is actually a special case of a Lagrangian duality result. Contrary to [1] we also consider the case that the set C is compact and convex and in this case we do not need to assume the standard regularity condition. http://repub.eur.nl/res/pub/1068/ 2003-12-03T00:00:00Z We consider equilibrium constrained optimization problems, which have a general formulationthat encompasses well-known models such as mathematical programs with equilibrium constraints, bilevel programs, and generalized semi-infinite programming problems. Based on the celebrated K K M lemma, we prove the existence of feasible points for the equilibrium constraints. Moreover, we analyze the topological and analytical structure of the feasible set. Alternative formulations of an equilibrium constrained optimization problem (ECOP) that are suitable for numerical purposes are also given. As an important _rst step for developing ef_cient algorithms, we provide a genericity analysis for the feasible set of a particular ECOP, for which all the functions are assumed to be linear.