Related papers: Mangasarian-Fromovitz-type constraint qualificatio…
The paper concerns the study of new classes of nonlinear and nonconvex optimization problems of the so-called infinite programming that are generally defined on infinite-dimensional spaces of decision variables and contain infinitely many…
When dealing with general Lipschitzian optimization problems, there are many problem classes where even weak constraint qualifications fail at local minimizers. In contrast to a constraint qualification, a problem qualification does not…
We consider a degenerate nonsmooth and nonconvex optimization problem for which the standard constraint qualification such as the generalized Mangasarian Fromovitz constraint qualification (GMFCQ) may not hold. We use smoothing functions…
Second-order optimality conditions for vector nonlinear programming problems with inequality constraints are studied in this paper. We introduce a new second-order constraint qualification, which includes Mangasarian-Fromovitz constraint…
Karush-Kuhn-Tucker (KKT) conditions for equality and inequality constrained optimization problems on smooth manifolds are formulated. Under the Guignard constraint qualification, local minimizers are shown to admit Lagrange multipliers. The…
We present new constraint qualification conditions for nonlinear semidefinite programming that extend some of the constant rank-type conditions from nonlinear programming. As an application of these conditions, we provide a unified global…
For an arbitrary finite family of semi-algebraic/definable functions, we consider the corresponding inequality constraint set and we study qualification conditions for perturbations of this set. In particular we prove that all positive…
In this paper we consider three minimization problems, namely quadratic, $\rho$-convex and quadratic fractional programing problems. The quadratic problem is considered with quadratic inequality constraints with bounded continuous and…
Second-order optimality conditions are essential for nonsmooth optimization, where both the objective and constraint functions are Lipschitz continuous and second-order directionally differentiable. This paper provides no-gap second-order…
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…
This article is devoted to the analysis of necessary and/or sufficient conditions for metric regularity in terms of Demyanov-Rubinov-Polyakova quasidifferentials. We obtain new necessary and sufficient conditions for the local metric…
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…
In this paper we deal with optimality conditions that can be verified by a nonlinear optimization algorithm, where only a single Lagrange multiplier is avaliable. In particular, we deal with a conjecture formulated in [R. Andreani, J.M.…
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…
This paper is devoted to establishing an enhanced Fritz John type first-order necessary condition for a general constrained nonlinear infinite-dimensional optimization problem. Unlike traditional constraint qualifications in optimization…
The paper is devoted to an analysis of a new constraint qualification and a derivation of the strongest existing optimality conditions for nonsmooth mathematical programming problems with equality and inequality constraints in terms of…
In the past years, augmented Lagrangian methods have been successfully applied to several classes of non-convex optimization problems, inspiring new developments in both theory and practice. In this paper we bring most of these recent…
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…
The literature on stochastic programming typically restricts attention to problems that fulfill constraint qualifications. The literature on estimation and inference under partial identification frequently restricts the geometry of…
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.…