Mathematical programs with vanishing constraints constitute a new class of difficult optimization problems with important applications in optimal topology design of mechanical structures. Vanishing constraints usually violate standard constraint qualifications, which gives rise to serious difficulties in theoretical and numerical treatment of these problems. In this work, we suggest several glo...

In this paper, we study the nonconvex nonsmooth optimization problem (P) of minimizing a tangentially convex function with inequality constraints where constraint functions are convex. This is done by using cone tangential subdifferentials together new qualification. Indeed, present qualification to guarantee that Karush-Kuhn-Tucker conditions necessary and sufficient for optimality (P). Moreov...

Many current deterministic solvers for NP-hard combinatorial optimization problems are based on nonlinear relaxation techniques that use floating point arithmetic. Occasionally, due to solving these relaxations, rounding errors may produce erroneous results, although the deterministic algorithm should compute the exact solution in a finite number of steps. This may occur especially if the relax...

In this paper, we study necessary optimality conditions for nonsmooth mathematical programs with equilibrium constraints. We first show that, unlike the smooth case, the Mathematical Program with Equilibrium Constraints Linear Independent Constraint Qualification is not a constraint qualification for the strong stationary condition when the objective function is nonsmooth. We argue that the str...

Mathematical programs with equilibrium (or complementarity) constraints, MPECs for short, is a difficult class of constrained optimization problems. The feasible set has a very special structure and violates most of the standard constraint qualifications (CQs). Thus, the standard KKT conditions are not necessary satisfied by minimizers and the convergence assumptions of many standard methods fo...

General and Professional Qualifications of Iranian High School Masters according to the Ministerial Documents H. Abdollaahi, Ph.D. A perusal of the ministerial documents at the Iranian Ministry of Education during the past 100 years was undertaken in order to clarify how the general and professional qualifications required for the post of high school master have evolved over the c...

In this paper, we study the mathematical program with equilibrium constraints (MPEC) formulated as a mathematical program with a parametric generalized equation involving the regular normal cone. Compared with the usual way of formulating MPEC through a KKT condition, this formulation has the advantage that it does not involve extra multipliers as new variables, and it usually requires weaker a...

789 www.cmj.hr Many African countries are liberal in accepting medical degrees and specialist qualifications acquired abroad. This in part stems from the lack of training programs on the African continent that can supply the required or near the required numbers of doctors to serve the populations. As the majority of African states are English-speaking, academic and professional qualifications ...

The paper concerns the study of new classes of nonlinear and nonconvex optimization problems of the so-called infinite programming that are generally defined on infinite-dimensional spaces of decision variables and contain infinitely many of equality and inequality constraints with arbitrary (may not be compact) index sets. These problems reduce to semi-infinite programs in the case of finite-d...