Related papers: Error bounds for rank constrained optimization pro…
In this paper, Lipschitz univariate constrained global optimization problems where both the objective function and constraints can be multiextremal are considered. The constrained problem is reduced to a discontinuous unconstrained problem…
We consider solving equality-constrained nonlinear, nonconvex optimization problems. This class of problems appears widely in a variety of applications in machine learning and engineering, ranging from constrained deep neural networks, to…
In this paper we propose a variant of the random coordinate descent method for solving linearly constrained convex optimization problems with composite objective functions. If the smooth part of the objective function has Lipschitz…
We propose a random-subspace algorithmic framework for global optimization of Lipschitz-continuous objectives, and analyse its convergence using novel tools from conic integral geometry. X-REGO randomly projects, in a sequential or…
We present a new feasible proximal gradient method for constrained optimization where both the objective and constraint functions are given by the summation of a smooth, possibly nonconvex function and a convex simple function. The…
This paper investigates a category of constrained fractional optimization problems that emerge in various practical applications. The objective function for this category is characterized by the ratio of a numerator and denominator, both…
Rank and cardinality penalties are hard to handle in optimization frameworks due to non-convexity and discontinuity. Strong approximations have been a subject of intense study and numerous formulations have been proposed. Most of these can…
Low-rank matrix completion consists of computing a matrix of minimal complexity that recovers a given set of observations as accurately as possible. Unfortunately, existing methods for matrix completion are heuristics that, while highly…
We present an adaptive online gradient descent algorithm to solve online convex optimization problems with long-term constraints , which are constraints that need to be satisfied when accumulated over a finite number of rounds T , but can…
The aim of this paper is to give a short overview on error bounds and to provide the first bricks of a unified theory. Inspired by the works of [8, 15, 13, 16, 10], we show indeed the centrality of the Lojasiewicz gradient inequality. For…
Online bilevel optimization (OBO) has emerged as a powerful framework for many machine learning problems. Prior works have developed several algorithms that minimize the standard bilevel local regret or the window-averaged bilevel local…
We study the sample complexity of the best-case Empirical Risk Minimizer in the setting of stochastic convex optimization. We show that there exists an instance in which the sample size is linear in the dimension, learning is possible, but…
Recently there were proposed some innovative convex optimization concepts, namely, relative smoothness [1] and relative strong convexity [2,3]. These approaches have significantly expanded the class of applicability of gradient-type methods…
Constrained Optimization solution algorithms are restricted to point based solutions. In practice, single or multiple objectives must be satisfied, wherein both the objective function and constraints can be non-convex resulting in multiple…
In many applications that require matrix solutions of minimal rank, the underlying cost function is non-convex leading to an intractable, NP-hard optimization problem. Consequently, the convex nuclear norm is frequently used as a surrogate…
In many applications that require matrix solutions of minimal rank, the underlying cost function is non-convex leading to an intractable, NP-hard optimization problem. Consequently, the convex nuclear norm is frequently used as a surrogate…
In this paper, we propose first-order feasible methods for difference-of-convex (DC) programs with smooth inequality and simple geometric constraints. Our strategy for maintaining feasibility of the iterates is based on a "retraction" idea…
In this paper we prove the local boundedness as well as the local Lipschitz continuity for solutions to a class of obstacle problems of the type $$\min\left\{\int_\Omega {F(x, Dz)}: z\in \mathcal{K}_{\psi}(\Omega)\right\}.$$ Here…
The standard assumption for proving linear convergence of first order methods for smooth convex optimization is the strong convexity of the objective function, an assumption which does not hold for many practical applications. In this…
Stochastic and adversarial data are two widely studied settings in online learning. But many optimization tasks are neither i.i.d. nor fully adversarial, which makes it of fundamental interest to get a better theoretical understanding of…