Related papers: Optimality Conditions for Variational Problems in …
Invariant conditions for conformable fractional problems of the calculus of variations under the presence of external forces in the dynamics are studied. Depending on the type of transformations considered, different necessary conditions of…
Minimax optimization problems arises from both modern machine learning including generative adversarial networks, adversarial training and multi-agent reinforcement learning, as well as from tradition research areas such as saddle point…
The paper is devoted to deriving necessary optimality conditions in a general optimal control problem for dynamical systems governed by controlled sweeping processes with hard-constrained control actions entering both polyhedral moving sets…
This paper focuses on second-order necessary optimality conditions for constrained optimization problems on Banach spaces. For problems in the classical setting, where the objective function is $C^2$-smooth, we show that strengthened…
In general, standard necessary optimality conditions cannot be formulated in a straightforward manner for semi-smooth shape optimization problems. In this paper, we consider shape optimization problems constrained by variational…
The aim of this paper is to exhibit a necessary and sufficient condition of optimality for functionals depending on fractional integrals and derivatives, on indefinite integrals and on presence of time delay. We exemplify with one example,…
The problem of minimizing convex functionals of probability distributions is solved under the assumption that the density of every distribution is bounded from above and below. A system of sufficient and necessary first-order optimality…
We study more general variational problems on time scales. Previous results are generalized by proving necessary optimality conditions for (i) variational problems involving delta derivatives of more than the first order, and (ii) problems…
We employ a fuzzy optimality condition for the Frechet subdifferential and some advanced techniques of variational analysis such as formulae for the subdifferentials of an infinite family of nonsmooth functions and the coderivative…
The paper is devoted to deriving novel second-order necessary and sufficient optimality conditions for local minimizers in rather general classes of nonsmooth unconstrained and constrained optimization problems in finite-dimensional spaces.…
In this paper, we establish the existence of the efficient solutions for polynomial vector optimization problems on a nonempty closed constraint set without any convexity and compactness assumptions. We first introduce the relative…
We obtain Euler-Lagrange and transversality optimality conditions for higher-order infinite horizon variational problems on a time scale. The new necessary optimality conditions improve the classical results both in the continuous and…
Constrained non-convex optimization is fundamentally challenging, as global solutions are generally intractable and constraint qualifications may not hold. However, in many applications, including safe policy optimization in control and…
This paper investigates the optimality conditions for characterizing the local minimizers of the constrained optimization problems involving an $\ell_p$ norm ($0<p<1$) of the variables, which may appear in either the objective or the…
In this paper, we discuss optimality conditions for optimization problems involving random state constraints, which are modeled in probabilistic or almost sure form. While the latter can be understood as the limiting case of the former, the…
This paper defines a convertible nonconvex function(CN function for short) and a weak (strong) uniform (decomposable, exact) CN function, proves the optimization conditions for their global solutions and proposes algorithms for solving the…
We derive a variant of the nonsmooth maximum principle for problems with pure state constraints. The interest of our result resides on the nonsmoothness itself since, when applied to smooth problems, it coincides with known results.…
This work proposes an implementable proximal-type method for a broad class of optimization problems involving nonsmooth and nonconvex objective and constraint functions. In contrast to existing methods that rely on an ad hoc model…
We provide a generalization of first-order necessary conditions of optimality for infinite-dimensional optimization problems with a finite number of inequality constraints and with a finite number of inequality and equality constraints. Our…
In this article we propose a new approach to an analysis of DC optimization problems. This approach was largely inspired by codifferential calculus and the method of codifferential descent and is based on the use of a so-called affine…