Related papers: Optimization Condition and Algorithm of Optimizati…
In this paper we obtain second- and first-order optimality conditions of Kuhn-Tucker type and Fritz John one for weak efficiency in the vector problem with inequality constraints. In the necessary conditions we suppose that the objective…
Functional constrained optimization is becoming more and more important in machine learning and operations research. Such problems have potential applications in risk-averse machine learning, semisupervised learning, and robust optimization…
We consider the convex optimization problem $\min \{f(x) : g_j(x)\leq 0, j=1,...,m\}$ where $f$ is convex, the feasible set K is convex and Slater's condition holds, but the functions $g_j$ are not necessarily convex. We show that for any…
Variational analysis provides the theoretical foundations and practical tools for constructing optimization algorithms without being restricted to smooth or convex problems. We survey the central concepts in the context of a concrete but…
This paper considers continuous-time coordination algorithms for networks of agents that seek to collectively solve a general class of nonsmooth convex optimization problems with an inherent distributed structure. Our algorithm design…
In this paper, we introduce faster accelerated primal-dual algorithms for minimizing a convex function subject to strongly convex function constraints. Prior to our work, the best complexity bound was $\mathcal{O}(1/{\varepsilon})$,…
Difference of convex (DC) functions cover a broad family of non-convex and possibly non-smooth and non-differentiable functions, and have wide applications in machine learning and statistics. Although deterministic algorithms for DC…
To solve convex optimization problems with a noisy gradient input, we analyze the global behavior of subgradient-like flows under stochastic errors. The objective function is composite, being equal to the sum of two convex functions, one…
An adaptive regularization algorithm using inexact function and derivatives evaluations is proposed for the solution of composite nonsmooth nonconvex optimization. It is shown that this algorithm needs at most…
In this paper, we propose two algorithms for solving convex optimization problems with linear ascending constraints. When the objective function is separable, we propose a dual method which terminates in a finite number of iterations. In…
In this paper, we present a conditional gradient type (CGT) method for solving a class of composite optimization problems where the objective function consists of a (weakly) smooth term and a (strongly) convex regularization term. While…
This paper is devoted to the study of approximate solutions for a multiobjective interval-valued optimization problem based on an interval order. We establish new existence theorems of approximate solutions for such a problem under some…
This paper proposes a new algorithm that solves non-convex optimal control problems with a theoretical guarantee for global convergence to a feasible local solution of the original problem. The proposed algorithm extends the recently…
Majorization-minimization algorithms consist of successively minimizing a sequence of upper bounds of the objective function so that along the iterations the objective function decreases. Such a simple principle allows to solve a large…
We develop new adaptive algorithms for variational inequalities with monotone operators, which capture many problems of interest, notably convex optimization and convex-concave saddle point problems. Our algorithms automatically adapt to…
In this paper we consider convex optimization problems with stochastic composite objective function subject to (possibly) infinite intersection of constraints. The objective function is expressed in terms of expectation operator over a sum…
Recent advancements in data science have significantly elevated the importance of orthogonally constrained optimization problems. The Riemannian approach has become a popular technique for addressing these problems due to the advantageous…
A new stochastic primal--dual algorithm for solving a composite optimization problem is proposed. It is assumed that all the functions/operators that enter the optimization problem are given as statistical expectations. These expectations…
Optimality conditions in the form of a variational inequality are proved for a class of constrained optimal control problems of stochastic differential equations. The cost function and the inequality constraints are functions of the…
We develop an efficient method for solving non-convex constrained optimization problems that are pervasive in economics. The optimal solution to these problems often involves randomization. We employ a Lagrangian framework and prove that…