Related papers: A Descent Method for Nonsmooth Multiobjective Opti…
This paper deals with approximate Pareto solutions of a nonsmooth interval-valued multiobjective optimization problem with data uncertainty in constraints. We first introduce some kinds of approximate Pareto solutions for the robust…
Multi-Objective Optimization (MOO) is an important problem in real-world applications. However, for a non-trivial problem, no single solution exists that can optimize all the objectives simultaneously. In a typical MOO problem, the goal is…
Most of existing neural methods for multi-objective combinatorial optimization (MOCO) problems solely rely on decomposition, which often leads to repetitive solutions for the respective subproblems, thus a limited Pareto set. Beyond…
The part of the analysis of the convergence rate of the mirror descent method that is connected with the adaptive time-varying step size rules due to Alkousa et al. (MOTOR 2024, pp. 3-18) is corrected. Moreover, a Lipschitz-free mirror…
We study multipoint Pad\'e approximants of type $(n,n)$ for the Hurwitz zeta function $f(a)=\zeta(s,a)$ with $\Re s>1$, constructed at quantile nodes $a_{n,j}=n\alpha_{n,j}$ generated by a real-analytic density $\kappa$ on…
A common goal in evolutionary multi-objective optimization is to find suitable finite-size approximations of the Pareto front of a given multi-objective optimization problem. While many multi-objective evolutionary algorithms have proven to…
The analysis of gradient descent-type methods typically relies on the Lipschitz continuity of the objective gradient. This generally requires an expensive hyperparameter tuning process to appropriately calibrate a stepsize for a given…
Decentralized optimization is a powerful paradigm that finds applications in engineering and learning design. This work studies decentralized composite optimization problems with non-smooth regularization terms. Most existing gradient-based…
This paper provides a novel framework for solving multiobjective discrete optimization problems with an arbitrary number of objectives. Our framework formulates these problems as network models, in that enumerating the Pareto frontier…
In this paper, we introduce some new iterative optimisation algorithms on Riemannian manifolds and Hilbert spaces which have good global convergence guarantees to local minima. More precisely, these algorithms have the following properties:…
The steepest descent method proposed by Fliege et al. motivates the research on descent methods for multiobjective optimization, which has received increasing attention in recent years. However, empirical results show that the Armijo line…
In this paper we consider large-scale composite optimization problems having the objective function formed as a sum of two terms (possibly nonconvex), one has (block) coordinate-wise Lipschitz continuous gradient and the other is…
This paper examines a variety of classical optimization problems, including well-known minimization tasks and more general variational inequalities. We consider a stochastic formulation of these problems, and unlike most previous work, we…
Composite optimization offers a powerful modeling tool for a variety of applications and is often numerically solved by means of proximal gradient methods. In this paper, we consider fully nonconvex composite problems under only local…
We propose a reachability approach for infinite and finite horizon multi-objective optimization problems for low-thrust spacecraft trajectory design. The main advantage of the proposed method is that the Pareto front can be efficiently…
The goal of multi-objective optimization is to understand optimal trade-offs between competing objective functions by finding the Pareto front, i.e., the set of all Pareto optimal solutions, where no objective can be improved without…
This paper aims at developing two versions of the generalized Newton method to compute not merely arbitrary local minimizers of nonsmooth optimization problems but just those, which possess an important stability property known as tilt…
Multi-objective optimization is central to many engineering and machine learning applications, where multiple objectives must be optimized in balance. While multi-gradient based optimization methods combine these objectives in each step,…
This paper addresses stochastic optimization of Lipschitz-continuous, nonsmooth and nonconvex objectives over compact convex sets, where only noisy function evaluations are available. While gradient-free methods have been developed for…
Recent advances in large-margin classification of data residing in general metric spaces (rather than Hilbert spaces) enable classification under various natural metrics, such as string edit and earthmover distance. A general framework…