Related papers: Regularized Multiobjective Optimization with Direc…
In this paper, we investigate the multi-objective optimal control problem of ordinary differential equations on Riemannian manifolds. We first obtain the second-order necessary conditions for weak Pareto optimal solutions for…
This paper introduces a novel double regularization scheme for bilevel optimization problems whose lower-level problem is composite and convex, but not necessarily strongly convex, in the lower-level variable. The analysis focuses on the…
This paper addresses the study of derivative-free smooth optimization problems, where the gradient information on the objective function is unavailable. Two novel general derivative-free methods are proposed and developed for minimizing…
This paper sheds new light on regularity of multifunctions through various characterizations of directional H\"older /Lipschitz metric regularity, which are based on the concepts of slope and coderivative. By using these characterizations,…
To solve convex optimization problems with a noisy gradient input, we analyze the global behavior of subgradient-like flows under stochastic errors. The objective function is composite, being equal to the sum of two convex functions, one…
The paper deals with a comprehensive theory of mappings, whose local behavior can be described by means of linear subspaces, contained in the graphs of two (primal and dual) generalized derivatives. This class of mappings includes the…
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…
Approximate necessary optimality conditions in terms of Fr\'echet subgradients and normals for a rather general optimization problem with a potentially non-Lipschitzian objective function are established with the aid of Ekeland's…
Optimization problems arising in data science have given rise to a number of new derivative-based optimization methods. Such methods often use standard smoothness assumptions -- namely, global Lipschitz continuity of the gradient function…
We report on new techniques and results in the regularity theory of general non-uniformly elliptic variational integrals. By means of a new potential theoretic approach we reproduce, in the non-uniformly elliptic setting, the optimal…
We consider problems with multiple linear objectives and linear constraints and use Adjustable Robust Optimization and Polynomial Optimization as tools to approximate the Pareto set with polynomials of arbitrarily large degree. The main…
Multi-objective learning under user-specified preference is common in real-world problems such as multi-lingual speech recognition under fairness. In this work, we frame such a problem as a semivectorial bilevel optimization problem, whose…
Multi-modal multi-objective optimization aims to find all Pareto optimal solutions including overlapping solutions in the objective space. Multi-modal multi-objective optimization has been investigated in the evolutionary computation…
We consider a stochastic version of the proximal point algorithm for optimization problems posed on a Hilbert space. A typical application of this is supervised learning. While the method is not new, it has not been extensively analyzed in…
(Renegar, 2016) introduced a novel approach to transforming generic conic optimization problems into unconstrained, uniformly Lipschitz continuous minimization. We introduce {\it radial transformations} generalizing these ideas, equipped…
In this paper, we introduce, in a Hilbert space setting, a second order dynamical system with asymptotically vanishing damping and vanishing Tikhonov regularization that approaches a multiobjective optimization problem with convex and…
In these notes, we present a general result concerning the Lipschitz regularity of a certain type of set-valued maps often found in constrained optimization and control problems. The class of multifunctions examined in this paper is…
This paper presents a detailed theoretical analysis of the three stochastic approximation proximal gradient algorithms proposed in our companion paper [49] to set regularization parameters by marginal maximum likelihood estimation. We prove…
Binary optimization, a representative subclass of discrete optimization, plays an important role in mathematical optimization and has various applications in computer vision and machine learning. Usually, binary optimization problems are…
The paper is devoted to deriving novel second-order necessary and sufficient optimality conditions for local minimizers in rather general classes of nonsmooth unconstrained and constrained optimization problems in finite-dimensional spaces.…