Related papers: The Karush-Kuhn-Tucker Optimality Conditions for M…
We establish new results of first-order necessary conditions of optimality for finite-dimensional problems with inequality constraints and for problems with equality and inequality constraints, in the form of John's theorem and in the form…
In this study, we examine Fritz John (FJ) and Karush-Kuhn-Tucker (KKT) type optimality conditions for a class of nonsmooth and nonconvex optimization problems with inequality constraints, where the objective and constraint functions all are…
We prove global Schauder estimates for kinetic Kolmogorov equations with coefficients that are H\"older continuous in the spatial variables but only measurable in time. Compared to other available results in the literature, our estimates…
Under study are some vector optimization problems over the space of Minkowski balls, i.e., symmetric convex compact subsets in Euclidean space. A typical problem requires to achieve the best result in the presence of conflicting goals;…
This paper on the whole concerns with the duality of Mayer problem for k-th order differential inclusions, where k is an arbitrary natural number. Thus, this work for constructing the dual problems to differential inclusions of any order…
In this work, we derive second-order optimality conditions for nonlinear semidefinite programming (NSDP) problems, by reformulating it as an ordinary nonlinear programming problem using squared slack variables. We first consider the…
In this paper, we study a nonsmooth/nonconvex multiobjective optimization problem with uncertain constraints in arbitrary Asplund spaces. We first provide necessary optimality condition in a fuzzy form for approximate weakly robust…
In the first part of this paper, inspired by the geometric method of Jean-Pierre Marec, we consider the two-impulse Hohmann transfer problem between two coplanar circular orbits as a constrained nonlinear programming problem. By using the…
This paper is concerned with the axiomatic foundation and explicit construction of a general class of optimality criteria that can be used for investment problems with multiple time horizons, or when the time horizon is not known in…
We present a systematic introduction to first-order optimality conditions for mathematical programs with equilibrium constraints (MPECs), emphasizing the limitations of classical nonlinear programming techniques. The goal is twofold. First,…
This paper is concerned with the sensitivity analysis of a class of parameterized fixed-point problems that arise in the context of obstacle-type quasi-variational inequalities. We prove that, if the operators in the considered fixed-point…
This paper aims to provide a series of characterizations of the robust isolated calmness of the Karush-Kuhn-Tucker (KKT) mapping for spectral norm regularized convex optimization problems. By establishing the variational properties of the…
In the last two decades, the sequential optimality conditions, which do not require constraint qualifications and allow improvement on the convergence assumptions of algorithms, had been considered in the literature. It includes the work by…
This paper studies bilevel polynomial optimization problems. To solve them, we give a method based on polynomial optimization relaxations. Each relaxation is obtained from the Kurash-Kuhn-Tucker (KKT) conditions for the lower level…
Storage-concerned economic dispatch (ED) problems with complementarity constraints are strongly non-convex and hard to solve because traditional Karush-Kuhn-Tucker (KKT) conditions do not hold in this condition. In our recent paper, we…
In this paper, we study nonconvex constrained optimization problems with both equality and inequality constraints, covering deterministic and stochastic settings. We propose a novel first-order algorithm framework that employs a…
Kuhn-Tucker conditions for mathematical programming problems in Banach spaces partially ordered by cone with empty interior are obtained under strong simultaneity condition. If partial ordered cone has interior point, it is proved that…
This paper studies duality and optimality conditions for general convex stochastic optimization problems. The main result gives sufficient conditions for the absence of a duality gap and the existence of dual solutions in a locally convex…
It is a very challenging task to identify the objectives on which a certain decision was based, in particular if several, potentially conflicting criteria are equally important and a continuous set of optimal compromise decisions exists.…
In this paper, we provide conditions under which one can take derivatives of the solution to convex optimization problems with respect to problem data. These conditions are (roughly) that Slater's condition holds, the functions involved are…