Mathematical Programs with Cardinality Constraints: Reformulation by Complementarity-Type Conditions and a Regularization Method
نویسندگان
چکیده
منابع مشابه
Mathematical Programs with Cardinality Constraints: Reformulation by Complementarity-Type Conditions and a Regularization Method
Optimization problems with cardinality constraints are very difficult mathematical programs which are typically solved by global techniques from discrete optimization. Here we introduce a mixed-integer formulation whose standard relaxation still has the same solutions (in the sense of global minima) as the underlying cardinality-constrained problem; the relation between the local minima is also...
متن کاملRegularization Method for Stochastic Mathematical Programs with Complementarity Constraints
In this paper, we consider a class of stochastic mathematical programs with equilibrium constraints (SMPECs) that has been discussed by Lin and Fukushima (2003). Based on a reformulation given therein, we propose a regularization method for solving the problems. We show that, under a weak condition, an accumulation point of the generated sequence is a feasible point of the original problem. We ...
متن کاملA New Regularization Method for Mathematical Programs with Complementarity Constraints with Strong Convergence Properties
Mathematical programs with equilibrium (or complementarity) constraints, MPECs for short, form a difficult class of optimization problems. The feasible set has a very special structure and violates most of the standard constraint qualifications. Therefore, one typically applies specialized algorithms in order to solve MPECs. One very prominent class of specialized algorithms are the regularizat...
متن کاملSemismooth Newton method for the lifted reformulation of mathematical programs with complementarity constraints
We consider a reformulation of mathematical programs with complementarity constraints, where by introducing an artificial variable the constraints are converted into equalities which are once but not twice differentiable. We show that the Lagrange optimality system of such a reformulation is semismooth and BD-regular at the solution under reasonable assumptions. Thus, fast local convergence can...
متن کاملLevenberg-Marquardt Method for Mathematical Programs with Linearly Complementarity Constraints
In this paper, a new method for solving a mathematical programming problem with linearly complementarity constraints (MPLCC) is introduced, which applies the Levenberg-Marquardt (L-M) method to solve the B-stationary condition of original problem. Under the MPEC-LICQ, the proposed method is proved convergent to B-stationary point of MPLCC.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: SIAM Journal on Optimization
سال: 2016
ISSN: 1052-6234,1095-7189
DOI: 10.1137/140978077