Related papers: On the multiplier rules
This paper is concerned with a class of stochastic optimization problems defined on a Banach space with almost sure conic-type constraints. For this class of problems, we investigate the consistency of optimal values and solutions…
In this article we consider a convex feasible set described by inequality constraints that are continuous and not necessarily Lipschitz or convex. We show that if the Slater constraint qualification and a non-degeneracy condition are…
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…
This paper addresses the class of continuous-time nonlinear programming problems with equality and inequality constraints. The paper presents necessary optimality conditions of the sequential form. To be more precise, a sequence of…
We extend Polyak's theorem on the convexity of joint numerical range from three to any number of quadratic forms on condition that they can be generated by three quadratic forms with a positive definite linear combination. Our new result…
We introduce a discrete-time fractional calculus of variations. First and second order necessary optimality conditions are established. Examples illustrating the use of the new Euler-Lagrange and Legendre type conditions are given. They…
The classical method to solve a quadratic optimization problem with nonlinear equality constraints is to solve the Karush-Kuhn-Tucker (KKT) optimality conditions using Newton's method. This approach however is usually computationally…
In this paper, we introduce a kind of approximate Karush--Kuhn--Tucker condition (AKKT) for a smooth cone-constrained vector optimization problem. We show that, without any constraint qualification, the AKKT condition is a necessary for a…
The purpose of this paper is to characterize the weak efficient solutions, the efficient solutions, and the isolated efficient solutions of a given vector optimization problem with finitely many convex objective functions and infinitely…
Minimax optimization problems are an important class of optimization problems arising from both modern machine learning and from traditional research areas. We focus on the stability of constrained minimax optimization problems based on the…
We consider two well-known problems: upper bounding the volume of lower dimensional ellipsoids contained in convex bodies given their John ellipsoid, and lower bounding the volume of ellipsoids containing projections of convex bodies given…
This work is a continuation of the previous one in [{\it Optimization} (2023)], where the existence of optimal solutions and first-order necessary optimality conditions in both Pontryagin's maximum principle form and the variational form…
Partial calmness is a celebrated but restrictive property of bilevel optimization problems whose presence opens a way to the derivation of Karush--Kuhn--Tucker-type necessary optimality conditions in order to characterize local minimizers.…
In this paper we consider the minimization of a continuous function that is potentially not differentiable or not twice differentiable on the boundary of the feasible region. By exploiting an interior point technique, we present first- and…
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…
Let $\mathcal{H}^{*}=\{h_1,h_2,\ldots\}$ be an ordered set of integers. We give sufficient conditions for the existence of increasing sequences of natural numbers $a_j$ and $n_k$ such that $n_k+h_{a_j}$ is a sum of two squares for every…
In the first part of this doctoral thesis we develop a regularity theory for a polyconvex functional in compressible elasticity. In the second part, we will concentrate on uniqueness questions in various situations of finite elasticity.…
[REVISED VERSION] The aim of this paper is to state a sharp version of the K\"onig supremum theorem, an equivalent reformulation of the Hahn--Banach theorem. We apply it to derive statements of the Lagrange multipliers, Karush-Kuhn-Tucker…
This paper characterizes the well-posedness of Karush-Kuhn-Tucker system for perturbed composite optimization. Using the parabolic regularity, we introduce a novel second-order variational function, shown to be the pivotal object governing…
This paper deals with approximate solutions of an optimization problem with interval-valued objective function. Four types of approximate solution concepts of the problem are proposed by considering the partial ordering $LU$ on the set of…