Related papers: Biobjective optimization with M-convex functions
Multi-objective optimization is a widely studied problem in diverse fields, such as engineering and finance, that seeks to identify a set of non-dominated solutions that provide optimal trade-offs among competing objectives. However, the…
This paper presents an algorithm for solving multiobjective optimization problems involving composite functions, where we minimize a quadratic model that approximates $F(x) - F(x^k)$ and that can be derivative-free. We establish theoretical…
In this paper we propose a variant of the random coordinate descent method for solving linearly constrained convex optimization problems with composite objective functions. If the smooth part of the objective function has Lipschitz…
When faced with multiple minima of an "inner-level" convex optimization problem, the convex bilevel optimization problem selects an optimal solution which also minimizes an auxiliary "outer-level" convex objective of interest. Bilevel…
Real-world optimization problems often do not just involve multiple objectives but also uncertain parameters. In this case, the goal is to find Pareto-optimal solutions that are robust, i.e., reasonably good under all possible realizations…
We present a new inverse optimization methodology for multi-objective convex optimization that accommodates an input solution that may not be Pareto optimal and determines a weight vector that produces a Pareto optimal solution that…
Convex optimization is a well-established research area with applications in almost all fields. Over the decades, multiple approaches have been proposed to solve convex programs. The development of interior-point methods allowed solving a…
Pareto optimization via evolutionary multi-objective algorithms has been shown to efficiently solve constrained monotone submodular functions. Traditionally when solving multiple problems, the algorithm is run for each problem separately.…
In this article, we use the monotonic optimization approach to propose an outcome-space outer approximation by copolyblocks for solving strictly quasiconvex multiobjective programming problems and especially in the case that the objective…
In this paper, we propose a generalized conditional gradient method for multiobjective optimization, which can be viewed as an improved extension of the classical Frank-Wolfe (conditional gradient) method for single-objective optimization.…
Like most multiobjective combinatorial optimization problems, biobjective optimization problems on matroids are in general intractable and their corresponding decision problems are in general NP-hard. In this paper, we consider biobjective…
The paper is devoted to the study of regularized versions of multiobjective optimization problems described by directionally Lipschitzian functions. Such regularizations appear in proximal-type algorithms of multiobjective optimization,…
For a linear equality constrained convex optimization problem involving two objective functions with a ``nonsmooth" + ``nonsmooth" composite structure, we study two algorithms derived from a mixed-order dynamical system which incorporates…
We study a bi-objective optimization problem, which for a given positive real number $n$ aims to find a vector $X = \{x_0,\cdots,x_{k-1}\} \in \mathbb{R}^{k}_{\ge 0}$ such that $\sum_{i=0}^{k-1} x_i = n$, minimizing the maximum of $k$…
The efficient optimization method for locally Lipschitz continuous multiobjective optimization problems from [1] is extended from finite-dimensional problems to general Hilbert spaces. The method iteratively computes Pareto critical points,…
This paper considers decentralized optimization of convex functions with mixed affine equality constraints involving both local and global variables. Constraints on global variables may vary across different nodes in the network, while…
In this paper, we address the problem of minimizing a convex function f over a convex set, with the extra constraint that some variables must be integer. This problem, even when f is a piecewise linear function, is NP-hard. We study an…
This paper is devoted to general nonconvex problems of multiobjective optimization in Hilbert spaces. Based on Mordukhovich's limiting subgradients, we define a new notion of Pareto critical points for such problems, establish necessary…
Recent years have seen a growing interest in accelerating optimization algorithms with machine-learned predictions. Sakaue and Oki (NeurIPS 2022) have developed a general framework that warm-starts the L-convex function minimization method…
This article investigates the approximation quality achievable for biobjective minimization problems with respect to the Pareto cone by solutions that are (approximately) optimal with respect to larger ordering cones. When simultaneously…