Related papers: A Homotopy Framework for Constrained Multiobjectiv…
The Homotopy paradigm, a general principle for solving challenging problems, appears across diverse domains such as robust optimization, global optimization, polynomial root-finding, and sampling. Practical solvers for these problems…
Optimizing the performance of many objectives (instantiated by tasks or clients) jointly with a few Pareto stationary solutions (models) is critical in machine learning. However, previous multi-objective optimization methods often focus on…
We introduce Entropy-Guided Multiplicative Updates (EGMU), a convex optimization framework for constructing multi-factor target-exposure portfolios by minimizing Kullback-Leibler divergence from a benchmark under linear factor constraints.…
A traditional and intuitively appealing Multi-Task Multiple Kernel Learning (MT-MKL) method is to optimize the sum (thus, the average) of objective functions with (partially) shared kernel function, which allows information sharing amongst…
This paper introduces a new method for solving quadratic programs using primal-dual interior-point methods. Instead of handling complementarity as an explicit equation in the Karush-Kuhn-Tucker (KKT) conditions, we ensure that…
Differentiating through constrained optimization problems is increasingly central to learning, control, and large-scale decision-making systems, yet practical integration remains challenging due to solver specialization and interface…
In this paper we propose a method that uses Lagrange multipliers and numerical algebraic geometry to find all critical points, and therefore globally solve, polynomial optimization problems. We design a polyhedral homotopy algorithm that…
In this paper, a tunneling method is developed for nonlinear multiobjective optimization problems using some ideas of the single objective tunneling method. The proposed method does not require any a priori chosen parameters or ordering…
Many scientific and engineering applications feature nonsmooth convex minimization problems over convex sets. In this paper, we address an important instance of this broad class where we assume that the nonsmooth objective is equipped with…
Quadratic programmingis a class of constrained optimization problem with quadratic objective functions and linear constraints. It has applications in many areas and is also used to solve nonlinear optimization problems. This article focuses…
In this paper, we introduce a homotopy function to trace the trajectory by applying modified homotopy continuation method for finding the solution of two-person zero-sum discounted stochastic ARAT game. We show that the algorithm has the…
We consider a PDE-constrained optimization problem of tracking type with parabolic state equation. The solution to the problem is characterized by the Karush-Kuhn-Tucker (KKT) system, which we formulate using a strong variational…
We propose a homotopy method for solving mathematical programs with complementarity constraints (CCs). The indicator function of the CCs is relaxed by a Lasry-Lions double envelope, an extension of the Moreau envelope that enjoys an…
In this article, a globally convergent sequential quadratic programming (SQP) method is developed for multi-objective optimization problems with inequality type constraints. A feasible descent direction is obtained using a linear…
In this article, we consider nonlinear complementarity problem. We introduce a new homotopy function for finding the solution of nonlinear complementarity problem through the trajectory . We show that the homotopy path approaching the…
This paper introduces the distributed Halpern Peaceman--Rachford (dHPR) method, an efficient algorithm for solving distributed convex composite optimization problems with non-smooth objectives, which achieves a non-ergodic $O(1/k)$…
Many-to-many matching seeks to match multiple points in one set and multiple points in another set, which is a basis for a wide range of data mining problems. It can be naturally recast in the framework of Optimal Transport (OT). However,…
In multi-objective optimization, a single decision vector must balance the trade-offs between many objectives. Solutions achieving an optimal trade-off are said to be Pareto optimal: these are decision vectors for which improving any one…
Multigraph matching is a recent variant of the graph matching problem. In this framework, the optimization procedure considers several graphs and enforces the consistency of the matches along the graphs. This constraint can be formalized as…
Achieving a just and sustainable transition requires the pursuit of multiple social and environmental targets. Two primary barriers impede this process: (1) targets are often in conflict with each other, and (2) policies aimed at these…