相关论文: Barzilai-Borwein Descent Methods for Multiobjectiv…

In this paper, we consider non-convex multi-block bilevel optimization (MBBO) problems, which involve $m\gg 1$ lower level problems and have important applications in machine learning. Designing a stochastic gradient and controlling its…

We develop a new Riemannian descent algorithm that relies on momentum to improve over existing first-order methods for geodesically convex optimization. In contrast, accelerated convergence rates proved in prior work have only been shown to…

Many real world scientific and industrial applications require optimizing multiple competing black-box objectives. When the objectives are expensive-to-evaluate, multi-objective Bayesian optimization (BO) is a popular approach because of…

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…

In this paper, we consider a formulation of nonlinear constrained optimization problems. We reformulate it as a time-varying optimization using continuous-time parametric functions and derive a dynamical system for tracking the optimal…

Multi-objective learning (MOL) problems often arise in emerging machine learning problems when there are multiple learning criteria, data modalities, or learning tasks. Different from single-objective learning, one of the critical…

Inspired by the recent paper (L. Ying, Mirror descent algorithms for minimizing interacting free energy, Journal of Scientific Computing, 84 (2020), pp. 1-14),we explore the relationship between the mirror descent and the variable metric…

In this paper, we study the Multi-Objective Bi-Level Optimization (MOBLO) problem, where the upper-level subproblem is a multi-objective optimization problem and the lower-level subproblem is for scalar optimization. Existing gradient-based…

Multi-objective Bayesian optimization (MOBO) provides a principled framework for optimizing expensive black-box functions with multiple objectives. However, existing MOBO methods often struggle with coverage, scalability with respect to the…

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…

Learning representation from relative similarity comparisons, often called ordinal embedding, gains rising attention in recent years. Most of the existing methods are batch methods designed mainly based on the convex optimization, say, the…

Multi-material design optimization problems can, after discretization, be solved by the iterative solution of simpler sub-problems which approximate the original problem at an expansion point to first order. In particular, models…

Bayesian Optimization (BO) is a powerful tool for optimizing expensive black-box objective functions. While extensive research has been conducted on the single-objective optimization problem, the multi-objective optimization problem remains…

Many real-world optimization problems such as engineering design can be eventually modeled as the corresponding multiobjective optimization problems (MOPs) which must be solved to obtain approximate Pareto optimal fronts. Multiobjective…

Many optimization problems require balancing multiple conflicting objectives. As gradient descent is limited to single-objective optimization, we introduce its direct generalization: Jacobian descent (JD). This algorithm iteratively updates…

Bayesian optimization (BO) is a popular global optimization scheme for sample-efficient optimization in domains with expensive function evaluations. The existing BO techniques are capable of finding a single global optimum solution.…

This study presents a novel Equiangular Direction Method (EDM) to solve a multi-objective optimization problem. We consider optimization problems, where multiple differentiable losses have to be minimized. The presented method computes…

We introduce an efficient and scalable method for density-based multi-material topology optimization, integrating classical mirror descent techniques with point-wise polytopal design constraints. Such constraints arise naturally in this…

The majority of First Order methods for large-scale convex-concave saddle point problems and variational inequalities with monotone operators are proximal algorithms which at every iteration need to minimize over problem's domain X the sum…

This paper is devoted to minimizing the sum of a smooth function and a nonsmooth $\ell_1$-regularized term. This problem as a special cases includes the $\ell_1$-regularized convex minimization problem in signal processing, compressive…