Related papers: Barzilai-Borwein Descent Methods for Multiobjectiv…
Motivated by variational inference methods, we propose a zeroth-order algorithm for solving optimization problems in the space of Gaussian probability measures. The algorithm is based on an interacting system of Gaussian particles that…
Machine learning problems with multiple objective functions appear either in learning with multiple criteria where learning has to make a trade-off between multiple performance metrics such as fairness, safety and accuracy; or, in…
The present paper studies a kind of robust optimization problems with constraint. The problem is formulated through Backward Stochastic Differential Equations (BSDEs) with quadratic generators. A necessary condition is established for the…
Multi-objective optimization (MOO) aims to optimize multiple, possibly conflicting objectives with widespread applications. We introduce a novel interacting particle method for MOO inspired by molecular dynamics simulations. Our approach…
We introduce a generalization of the linearized Alternating Direction Method of Multipliers to optimize a real-valued function $f$ of multiple arguments with potentially multiple constraints $g_\circ$ on each of them. The function $f$ may…
Multi-objective optimization (MOO) lies at the core of many machine learning (ML) applications that involve multiple, potentially conflicting objectives (e.g., multi-task learning, multi-objective reinforcement learning, among many others).…
In this work, we further develop multigoal-oriented a posteriori error estimation with two objectives in mind. First, we formulate goal-oriented mesh adaptivity for multiple functionals of interest for nonlinear problems in which both the…
This paper is concerned with a lesser-studied problem in the context of model-based, uncertainty quantification (UQ), that of optimization/design/control under uncertainty. The solution of such problems is hindered not only by the usual…
This work introduces a new cubic regularization method for nonconvex unconstrained multiobjective optimization problems. At each iteration of the method, a model associated with the cubic regularization of each component of the objective…
Bayesian optimization (BO) is a leading method for optimizing expensive black-box optimization and has been successfully applied across various scenarios. However, BO suffers from the curse of dimensionality, making it challenging to scale…
Geometric programming problems occur frequently in engineering design and management. In multiobjective optimization, the trade-off information between different objective functions is probably the most important piece of information in a…
We develop an adaptive-metric framework for norm-minimization-based outer approximation algorithms in bounded convex vector optimization. The key idea is to let the scalarization metric vary across iterations while measuring approximation…
Based on the ideas of arXiv:1710.06612, we consider the problem of minimization of the Holder-continuous non-smooth functional $f$ with non-positive convex (generally, non-smooth) Lipschitz-continuous functional constraint. We propose some…
The alternating direction method of multipliers (ADMM) is a versatile tool for solving a wide range of constrained optimization problems, with differentiable or non-differentiable objective functions. Unfortunately, its performance is…
The multi-gradient descent algorithm (MGDA) finds a common descent direction that can improve all objectives by identifying the minimum-norm point in the convex hull of the objective gradients. This method has become a foundational tool in…
Existing motion planning methods often have two drawbacks: 1) goal configurations need to be specified by a user, and 2) only a single solution is generated under a given condition. In practice, multiple possible goal configurations exist…
Meta learning with multiple objectives can be formulated as a Multi-Objective Bi-Level optimization Problem (MOBLP) where the upper-level subproblem is to solve several possible conflicting targets for the meta learner. However, existing…
In this paper, we develop a global descent method for non-convex multi-objective optimization problems. The proposed approach builds upon foundational concepts from single-objective global descent techniques while removing the need for…
Training machine learning models inherently involves a resource-intensive and noisy iterative learning procedure that allows epoch-wise monitoring of the model performance. However, the insights gained from the iterative learning procedure…
This paper proposes a nonmonotone proximal quasi-Newton algorithm for unconstrained convex multiobjective composite optimization problems. To design the search direction, we minimize the max-scalarization of the variations of the Hessian…