相关论文: Approximate stationarity in disjunctive optimizati…
Approximate stationarity conditions provide necessary optimality conditions without requiring additional assumptions by demanding that a perturbed stationarity system possesses solutions as the involved perturbations tend to zero. Together…
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.…
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…
Based on the tools of limiting variational analysis, we derive a sequential necessary optimality condition for nonsmooth mathematical programs which holds without any additional assumptions. In order to ensure that stationary points in this…
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…
In this paper, we investigate second-order necessary conditions and exact penalty of mathematical programs with switching constraints (MPSC). Some new second-order constraint qualifications and second-order quasi-normality are introduced…
Approximate necessary optimality conditions in terms of Fr\'echet subgradients and normals for a rather general optimization problem with a potentially non-Lipschitzian objective function are established with the aid of Ekeland's…
In this paper, we study the difficult class of optimization problems called the mathematical programs with vanishing constraints or MPVC. Extensive research has been done for MPVC regarding stationary conditions and constraint…
We show that, for a fixed order $\gamma\geq 1$, each local minimizer of a rather general nonsmooth optimization problem in Euclidean spaces is either M-stationary in the classical sense (corresponding to stationarity of order $1$),…
Asymptotic stationarity and regularity conditions turned out to be quite useful to study the qualitative properties of numerical solution methods for standard nonlinear and complementarity-constrained programs. In this paper, we first…
In this paper, we study a class of optimization problems, called Mathematical Programs with Cardinality Constraints (MPCaC). This kind of problem is generally difficult to deal with, because it involves a constraint that is not continuous…
In this paper, we consider the cardinality-constrained optimization problems and propose a new sequential optimality condition for the continuous relaxation reformulation which is popular recently. It is stronger than the existing results…
Constraint qualifications for a Mathematical Program with Equilibrium Constraints (MPEC) are essential for analyzing stationarity properties and establishing convergence results. In this paper, we explore several classical MPEC constraint…
This paper introduces and studies the optimal control problem with equilibrium constraints (OCPEC). The OCPEC is an optimal control problem with a mixed state and control equilibrium constraint formulated as a complementarity constraint and…
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…
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…
During the last years, asymptotic (or sequential) constraint qualifications, which postulate upper semicontinuity of certain set-valued mappings and provide a natural companion of asymptotic stationarity conditions, have been shown to be…
In this paper we consider a sufficiently broad class of nonlinear mathematical programs with disjunctive constraints, which, e.g., include mathematical programs with complemetarity/vanishing constraints. We present an extension of the…
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…
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…