Mathematical programs with vanishing constraints: constraint qualifications, their applications, and a new regularization method
نویسندگان
چکیده
منابع مشابه
Mathematical programs with vanishing constraints: optimality conditions and constraint qualifications
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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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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Mathematical programs with equilibrium (or complementarity) constraints, MPECs for short, are 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 Karush-Kuhn-Tucker (KKT) conditions are not necessarily satisfied by minimizers and the convergence assumptions of many meth...
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And out of the confusion Where the river meets the sea Something new would arrive Something better would arrive... " Acknowledgements The doctoral thesis at hand is the result of my research during the time as a Ph.D. student at the Department of Mathematics at the University of Würzburg. In a long-term project like this one, there are, of course, several ups and downs, and hence one is lucky t...
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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: Optimization
سال: 2018
ISSN: 0233-1934,1029-4945
DOI: 10.1080/02331934.2018.1542531