相关论文: Global aspects of the continuous reformulation for…
We extend the convergence analysis of the Scholtes-type regularization method for cardinality-constrained optimization problems. Its behavior is clarified in the vicinity of saddle points, and not just of minimizers as it has been done in…
We consider nonlinear optimization problems with cardinality constraints. Based on a continuous reformulation we introduce second order necessary and sufficient optimality conditions. Under such a second order condition, we can guarantee…
We study sparsity constrained nonlinear optimization (SCNO) from a topological point of view. Special focus will be on M-stationary points from Burdakov et al. (2016). We introduce nondegenerate M-stationary points and define their M-index.…
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…
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…
Cardinality constraints in optimization are commonly of $L^0$-type, and they lead to sparsely supported optimizers. An efficient way of dealing with these constraints algorithmically, when the objective functional is convex, is…
We study cardinality-constrained optimization problems (CCOP) in general position, i. e. those optimization-related properties that are fulfilled for a dense and open subset of their defining functions. We show that the well-known…
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…
For the rank regularized minimization problem, we introduce several kinds of stationary points by the problem itself and its equivalent reformulations including the mathematical program with an equilibrium constraint (MPEC), the global…
We study a cardinality-constrained optimization problem with nonnegative variables in this paper. This problem is often encountered in practice. Firstly we study some properties on the optimal solutions of this optimization problem under…
We consider the sparse optimization problem with nonlinear constraints and an objective function, which is given by the sum of a general smooth mapping and an additional term defined by the $ \ell_0 $-quasi-norm. This term is used to obtain…
We consider general nonlinear programming problems with cardinality constraints. By relaxing the binary variables which appear in the natural mixed-integer programming formulation, we obtain an almost equivalent nonlinear programming…
The paper addresses general constrained and non-linear optimization problems. For some of these notoriously hard problems, there exists a reformulation as an unconstrained, global optimization problem. We illustrate the transformation, and…
The goal of this paper is to compare alternative stationarity notions in structured nonsmooth optimization (SNO). Here, nonsmoothness is caused by complementarity, vanishing, orthogonality type, switching, or disjunctive constraints. On one…
This paper is devoted to studying the stationary solutions of a general constrained optimization problem through its associated unconstrained penalized problems. We aim to answer the question, "what do the stationary solutions of a…
This paper studies the properties of d-stationary points of the trimmed lasso (Luo et al., 2013, Huang et al., 2015, and Gotoh et al., 2018) and the composite optimization problem with the truncated nuclear norm (Gao and Sun, 2010, and…
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 $1$),…
In this paper, we focus on a class of convexly constrained nonsmooth convex-concave saddle point problems with cardinality penalties. Although such nonsmooth nonconvex-nonconcave and discontinuous min-max problems may not have a saddle…
Robust principal component analysis is an important representative method in data analysis. It is usually viewed as an optimization problem involving the rank and $\ell_0$-norm of matrices. In this paper, we study the rank and $\ell_0$…
Trace norm regularization is a widely used approach for learning low rank matrices. A standard optimization strategy is based on formulating the problem as one of low rank matrix factorization which, however, leads to a non-convex problem.…