Enhanced Fritz John stationarity, new constraint qualifications and local error bound for mathematical programs with vanishing constraints
نویسندگان
چکیده
منابع مشابه
Mathematical Programs with Equilibrium Constraints: Enhanced Fritz John-conditions, New Constraint Qualifications, and Improved Exact Penalty Results
Mathematical programs with equilibrium (or complementarity) constraints (MPECs for short) form a difficult class of optimization problems. The standard KKT conditions are not always necessary optimality conditions due to the fact that suitable constraint qualifications are often violated. Alternatively, one can therefore use the Fritz John-approach to derive necessary optimality conditions. Whi...
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We consider a difficult class of optimization problems that we call a mathematical program with vanishing constraints. Problems of this kind arise in various applications including optimal topology design problems of mechanical structures. We show that some standard constraint qualifications like LICQ and MFCQ usually do not hold at a local minimum of our program, whereas the Abadie constraint ...
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With the aid of some novel complementarity constraint quali cations, we derive some simpli ed primal-dual characterizations of a B-stationary point for a mathematical program with complementarity constraints (MPEC). The approach is based on a locally equivalent piecewise formulation of such a program near a feasible point. The simpli ed results, which rely heavily on a careful dissection and im...
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We introduce two new weaker Constraint Qualifications (CQs) for mathematical programs with equilibrium (or complementarity) constraints, MPEC for short. One of them is a tailored version of the constant rank of subspace component (CRSC) and the other is a relaxed version of the MPECNo Nonzero Abnormal Multiplier Constraint Qualification (MPEC-NNAMCQ). Both incorporate the exact set of gradients...
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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...
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ژورنال
عنوان ژورنال: Journal of Mathematical Analysis and Applications
سال: 2019
ISSN: 0022-247X
DOI: 10.1016/j.jmaa.2018.11.063