Related papers: Robust Optimization Approach for Solving Uncertain…
Stochastic multi-objective optimization (SMOO) has recently emerged as a powerful framework for addressing machine learning problems with multiple objectives. The bias introduced by the nonlinearity of the subproblem solution mapping…
Topology optimization under uncertainty (TOuU) often defines objectives and constraints by statistical moments of geometric and physical quantities of interest. Most traditional TOuU methods use gradient-based optimization algorithms and…
Local optimization presents a promising approach to expensive, high-dimensional black-box optimization by sidestepping the need to globally explore the search space. For objective functions whose gradient cannot be evaluated directly,…
Multiobjective optimization plays an increasingly important role in modern applications, where several criteria are often of equal importance. The task in multiobjective optimization and multiobjective optimal control is therefore to…
To date, the multi-objective optimization literature has mainly focused on conflicting objectives, studying the Pareto front, or requiring users to balance tradeoffs. Yet, in machine learning practice, there are many scenarios where such…
Bilevel optimization has been developed for many machine learning tasks with large-scale and high-dimensional data. This paper considers a constrained bilevel optimization problem, where the lower-level optimization problem is convex with…
In this work, we study the classical distributed optimization problem over digraphs, where the objective function is a sum of smooth local functions. Inspired by the implicit tracking mechanism proposed in our earlier work, we develop a…
The ability to deal with systems parametric uncertainties is an essential issue for heavy self-driving vehicles in unconfined environments. In this sense, robust controllers prove to be efficient for autonomous navigation. However,…
The problem we consider is a multi-objective optimization problem, in which the goal is to find an optimal value of a vector function representing various criteria. The aim of this work is to develop an algorithm which utilizes the trust…
We present a proximal gradient method for solving convex multiobjective optimization problems, where each objective function is the sum of two convex functions, with one assumed to be continuously differentiable. The algorithm incorporates…
Robust optimization is a framework for modeling optimization problems involving data uncertainty and during the last decades has been an area of active research. If we focus on linear programming (LP) problems with i) uncertain data, ii)…
We study the set of solutions to a parameterized, strongly convex optimization problem whose cost depends on uncertain, bounded parameters. We compute a certified outer approximation of the corresponding set of optimizers, using convergence…
In this paper, we consider an adaptive approach to address optimization problems with uncertain cost parameters. Here, the decision maker selects an initial decision, observes the realization of the uncertain cost parameters, and then is…
Performance analysis of first-order algorithms with inexact oracles has gained recent attention due to various emerging applications in which obtaining exact gradients is impossible or computationally expensive. Previous research has…
Robust optimization aims to find optimum points from the collection of points that are feasible for every possible scenario of a given uncertain set. An optimum solution to a robust optimization problem is commonly found by the min-max…
This article utilizes the projected gradient method (PG) for a non-negative matrix factorization problem (NMF), where one or both matrix factors must have orthonormal columns or rows. We penalise the orthonormality constraints and apply the…
Current state-of-the-art multi-objective optimization solvers, by computing gradients of all $m$ objective functions per iteration, produce after $k$ iterations a measure of proximity to critical conditions that is upper-bounded by…
We present the Multilevel Bregman Proximal Gradient Descent (ML BPGD) method, a novel multilevel optimization framework tailored to constrained convex problems with relative Lipschitz smoothness. Our approach extends the classical…
Multiobjective optimization plays an increasingly important role in modern applications, where several objectives are often of equal importance. The task in multiobjective optimization and multiobjective optimal control is therefore to…
In this paper we analyze several new methods for solving nonconvex optimization problems with the objective function formed as a sum of two terms: one is nonconvex and smooth, and another is convex but simple and its structure is known.…