相关论文: Solving mathematical programs with complementarity…
This paper is devoted to the study of the metric subregularity constraint qualification (MSCQ) for general optimization problems, with the emphasis on the nonconvex setting. We elaborate on notions of directional pseudo- and…
Mathematical programs with disjunctive constraints (MPDCs for short) cover several different problem classes from nonlinear optimization including complementarity-, vanishing-, cardinality-, and switching-constrained optimization problems.…
This paper examines solution methods for mathematical programs with complementarity constraints (MPCC) obtained from the time-discretization of optimal control problems (OCPs) subject to nonsmooth dynamical systems. The MPCC theory and…
For mathematical programs with complementarity constraints (MPCC), we study the stability properties of their Scholtes regularization. Our goal is to relate nondegenerate C-stationary points of MPCC with nondegenerate Karush-Kuhn-Tucker…
We consider the Mathematical Program with Complementarity Constraints (MPCC). One of the main challenges in solving this problem is the systematic failure of standard Constraint Qualifications (CQs). Carefully accounting for the…
Mathematical programs with or-constraints form a new class of disjunctive optimization problems with inherent practical relevance. In this paper, we provide a comparison of three different first-order methods for the numerical treatment of…
Our recent study (Lin and Ohtsuka, 2024) proposed a new penalty method for solving mathematical programming with complementarity constraints (MPCC). This method first reformulates MPCC as a parameterized nonlinear programming called gap…
In this paper, we are concerned with stationarity conditions and qualification conditions for optimization problems with disjunctive constraints. This class covers, among others, optimization problems with complementarity, vanishing, or…
Mathematical Program with Complementarity Constraints (MPCC) plays a very important role in many fields such as engineering design, economic equilibrium, multilevel game, and mathematical programming theory itself. In theory its constraints…
We consider the class of mathematical programs with orthogonality type constraints (MPOC). Orthogonality type constraints appear by reformulating the sparsity constraint via auxiliary binary variables and relaxing them afterwards. For MPOC…
We consider optimization problems with a disjunctive structure of the constraints. Prominent examples of such problems are mathematical programs with equilibrium constraints or vanishing constraints. Based on the concepts of directional…
Switching-constrained optimization problems form a difficult class of mathematical programs since their feasible set is almost disconnected while standard constraint qualifications are likely to fail at several feasible points. That is why…
In this paper, we give an overview on optimality conditions and exact penalization for the mathematical program with switching constraints (MPSC). MPSC is a new class of optimization problems which has some important applications. It is…
This study explores B-stationarity of mathematical programs with complementarity constraints (MPCCs) and convergence behavior of MPCC algorithms. Special attention is given to the cases with biactive complementarity constraints. First, we…
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. We derive a new necessary optimality…
We investigate a family of bilevel imaging learning problems where the lower-level instance corresponds to a convex variational model involving first- and second-order nonsmooth sparsity-based regularizers. By using geometric properties of…
We introduce new first-order necessary conditions for mathematical programs with complementarity constraints (MPCCs), which lie between strong and M-stationarity and have a relatively simple description. We show that they hold for local…
We introduce a novel class of regularization functions, called Cauchy-Schwarz (CS) regularizers, which can be designed to induce a wide range of properties in solution vectors of optimization problems. To demonstrate the versatility of CS…
It is known in the literature that local minimizers of mathematical programs with complementarity constraints (MPCCs) are so-called M-stationary points, if a weak MPCC-tailored Guignard constraint qualification (called MPCC-GCQ) holds. In…
Mathematical programs with complementarity constraints (MPCCs) are a challenging class of nonlinear optimization problems, because their nonlinear programming reformulations violate standard constraint qualifications at every feasible…