Related papers: On estimating the regular normal cone to constrain…
This paper investigates new first-order optimality conditions for general optimization problems. These optimality conditions are stronger than the commonly used M-stationarity conditions and are in particular useful when the latter cannot…
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 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…
The proximal, regular and limiting normal cones to the second-order cone complementarity set play important roles in studying mathematical programs with second-order cone complementarity constraints, second-order cone programs, and the…
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…
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…
New measures for the quantization of systems with constraints are discussed and applied to several examples, in particular, examples of alternative but equivalent formulations of given first-class constraints, as well as a comparison of…
We study randomized variants of two classical algorithms: coordinate descent for systems of linear equations and iterated projections for systems of linear inequalities. Expanding on a recent randomized iterated projection algorithm of…
We present necessary and sufficient optimality conditions for finite time optimal control problems for a class of hybrid systems described by linear complementarity models. Although these optimal control problems are difficult in general…
The well known constant rank constraint qualification [Math. Program. Study 21:110--126, 1984] introduced by Janin for nonlinear programming has been recently extended to a conic context by exploiting the eigenvector structure of the…
We present an analysis of sets of matrices with rank less than or equal to a specified number $s$. We provide a simple formula for the normal cone to such sets, and use this to show that these sets are prox-regular at all points with rank…
We study a generalization of conditional probability for arbitrary ordered vector spaces. A related problem is that of assigning a numerical value to one vector relative to another. We characterize the groups for which these generalized…
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…
The paper suggests a new --- to the best of the author's knowledge --- characterization of decisions which are optimal in the multi-objective optimization problem with respect to a definite proper preference cone, a Euclidean cone with a…
We give new computable necessary conditions for a class of optimal transportation problems to have smooth solutions.
We present recent advances in the analysis of constrained optimization problems with constraints given by singular mappings obtained within the framework of the $p$-regularity theory developed over the last twenty years. In particular, we…
Many contemporary applications in signal processing and machine learning give rise to structured non-convex non-smooth optimization problems that can often be tackled by simple iterative methods quite effectively. One of the keys to…
The aim of this paper is to give a simpler, more usable sufficient condition to the regularity of generic weakly stationary time series. Also, this condition is used to show how regular processes satisfying these sufficient conditions can…
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…
Conditional stability estimates require additional regularization for obtaining stable approximate solutions if the validity area of such estimates is not completely known. In this context, we consider ill-posed nonlinear inverse problems…