Related papers: Level-set methods for convex optimization

The minimization of convex functions which are only available through partial and noisy information is a key methodological problem in many disciplines. In this paper we consider convex optimization with noisy zero-th order information,…

In this paper, we study a class of stochastic bilevel optimization problems, also known as stochastic simple bilevel optimization, where we minimize a smooth stochastic objective function over the optimal solution set of another stochastic…

A vast majority of machine learning algorithms train their models and perform inference by solving optimization problems. In order to capture the learning and prediction problems accurately, structural constraints such as sparsity or low…

A common problem encountered in many real-world applications is level set estimation where the goal is to determine the region in the function domain where the function is above or below a given threshold. When the function is black-box and…

Coordinate descent algorithms solve optimization problems by successively performing approximate minimization along coordinate directions or coordinate hyperplanes. They have been used in applications for many years, and their popularity…

Stochastic gradient methods are scalable for solving large-scale optimization problems that involve empirical expectations of loss functions. Existing results mainly apply to optimization problems where the objectives are one- or two-level…

A polyhedral convex set optimization problem is given by a set-valued objective mapping from the $n$-dimensional to the $q$-dimensional Euclidean space whose graph is a convex polyhedron. This problem can be seen as the most elementary…

Bilevel optimization problems involve two nested objectives, where an upper-level objective depends on a solution to a lower-level problem. When the latter is non-convex, multiple critical points may be present, leading to an ambiguous…

Higher-order tensor methods were recently proposed for minimizing smooth convex and nonconvex functions. Higher-order algorithms accelerate the convergence of the classical first-order methods thanks to the higher-order derivatives used in…

Vector optimization problems are a generalization of multiobjective optimization in which the preference order is related to an arbitrary closed and convex cone, rather than the nonnegative octant. Due to its real life applications, it is…

The usual approach to developing and analyzing first-order methods for smooth convex optimization assumes that the gradient of the objective function is uniformly smooth with some Lipschitz constant $L$. However, in many settings the…

A wide range of applications arising in machine learning and signal processing can be cast as convex optimization problems. These problems are often ill-posed, i.e., the optimal solution lacks a desired property such as uniqueness or…

Synthesis of optimization algorithms typically follows a {\em design-then-analyze\/} approach, which can obscure fundamental performance limits and hinder the systematic development of algorithms that operate near these limits. Recently, a…

A new and simple method for quasi-convex optimization is introduced from which its various applications can be derived. Especially, a global optimum under constrains can be approximated for all continuous functions.

This study develops a framework for a class of constant modulus (CM) optimization problems, which covers binary constraints, discrete phase constraints, semi-orthogonal matrix constraints, non-negative semi-orthogonal matrix constraints,…

In this paper, vector optimization is considered in the framework of decision making and optimization in general spaces. Interdependencies between domination structures in decision making and domination sets in vector optimization are…

In this paper we consider stochastic composite convex optimization problems with the objective function satisfying a stochastic bounded gradient condition, with or without a quadratic functional growth property. These models include the…

Error bounds, which refer to inequalities that bound the distance of vectors in a test set to a given set by a residual function, have proven to be extremely useful in analyzing the convergence rates of a host of iterative methods for…

We consider solving large scale nonconvex optimisation problems with nonnegativity constraints. Such problems arise frequently in machine learning, such as nonnegative least-squares, nonnegative matrix factorisation, as well as problems…

We study a class of bilevel optimization problems in which both the upper- and lower-level problems have minimax structures. This setting captures a broad range of emerging applications. Despite the extensive literature on bilevel…