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We present two first-order, sequential optimization algorithms to solve constrained optimization problems. We consider a black-box setting with a priori unknown, non-convex objective and constraint functions that have Lipschitz continuous…
In this paper, by using tools of second-order variational analysis, we study the popular forward-backward splitting method with Beck-Teboulle's line-search for solving convex optimization problem where the objective function can be split…
We distinguish two kinds of piecewise linear functions and provide an interesting representation for a piecewise linear function between two normed spaces. Based on such a representation, we study a fully piecewise linear vector…
The paper provides global optimization algorithms for two particularly difficult nonconvex problems raised by hybrid system identification: switching linear regression and bounded-error estimation. While most works focus on local…
Motivated by applications in optimization and machine learning, we consider stochastic quasi-Newton (SQN) methods for solving stochastic optimization problems. In the literature, the convergence analysis of these algorithms relies on strong…
We develop a Frank-Wolfe algorithm with corrective steps, generalizing previous algorithms including blended conditional gradients, blended pairwise conditional gradients, and fully-corrective Frank-Wolfe. For this, we prove tight…
We present a finitely convergent cutting-plane algorithm for solving a general mixed-integer convex program given an oracle for solving a general convex program. This method is extended to solve a family of two-stage mixed-integer convex…
A key problem in multiobjective linear programming is to find the set of all efficient extreme points in objective space. In this paper we introduce oriented projective geometry as an efficient and effective framework for solving this…
Optimization problems with composite functions consist of an objective function which is the sum of a smooth and a (convex) nonsmooth term. This particular structure is exploited by the class of proximal gradient methods and some of their…
Many approaches for addressing Global Optimization problems typically rely on relaxations of nonlinear constraints over specific mathematical primitives. This is restricting in applications with constraints that are black-box, implicit or…
In recent years, by using Bregman distance, the Lipschitz gradient continuity and strong convexity were lifted and replaced by relative smoothness and relative strong convexity. Under the mild assumptions, it was proved that gradient…
Prediction+optimization is a common real-world paradigm where we have to predict problem parameters before solving the optimization problem. However, the criteria by which the prediction model is trained are often inconsistent with the goal…
We consider convex optimization problems with the objective function having Lipshitz-continuous $p$-th order derivative, where $p\geq 1$. We propose a new tensor method, which closes the gap between the lower…
Motivated by recent increased interest in optimization algorithms for non-convex optimization in application to training deep neural networks and other optimization problems in data analysis, we give an overview of recent theoretical…
In this paper, a class of optimization problems with nonlinear inequality constraints is discussed. Based on the ideas of sequential quadratic programming algorithm and the method of strongly sub-feasible directions, a new superlinearly…
We analyze combinatorial optimization problems with ordinal, i.e., non-additive, objective functions that assign categories (like good, medium and bad) rather than cost coefficients to the elements of feasible solutions. We review different…
This paper considers a general class of iterative optimization algorithms, referred to as linear-optimization-based convex programming (LCP) methods, for solving large-scale convex programming (CP) problems. The LCP methods, covering the…
Binary optimization is a central problem in mathematical optimization and its applications are abundant. To solve this problem, we propose a new class of continuous optimization techniques which is based on Mathematical Programming with…
This paper proposes novel algorithm for non-convex multimodal constrained optimisation problems. It is based on sequential solving restrictions of problem to sections of feasible set by random subspaces (in general, manifolds) of low…
This paper develops a method for obtaining guaranteed outer approximations for global attractors of continuous and discrete time nonlinear dynamical systems. The method is based on a hierarchy of semidefinite programming problems of…