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Vector optimization problems are a generalization of multiobjective optimization in which the preference order is related to an arbitrary closed and convex cone, rather than the nonnegative octant. Due to its real life applications, it is…

Optimization and Control · Mathematics 2013-12-03 J. Y. Bello Cruz , G. C. Bento , G. Bouza Allende , R. F. B. Costa

We develop a new proximal-gradient method for minimizing the sum of a differentiable, possibly nonconvex, function plus a convex, possibly non differentiable, function. The key features of the proposed method are the definition of a…

Numerical Analysis · Mathematics 2016-05-13 Silvia Bonettini , Ignace Loris , Federica Porta , Marco Prato

In this paper, in order to find critical points of vector-valued functions with respect to the partial order induced by a closed, convex, and pointed cone with nonempty interior, we propose a nonlinear modified Polak-Ribiere-Polyak type…

Optimization and Control · Mathematics 2024-04-15 Yushan Bai , Jiawei Chen , Kaiping Liu

In this paper, a globally convergent Newton-type proximal gradient method is developed for composite multi-objective optimization problems where each objective function can be represented as the sum of a smooth function and a nonsmooth…

Optimization and Control · Mathematics 2024-10-25 Md Abu Talhamainuddin Ansary

This paper presents an auto-conditioned proximal gradient method for nonconvex optimization. The method determines the stepsize using an estimation of local curvature and does not require any prior knowledge of problem parameters and any…

Optimization and Control · Mathematics 2025-09-19 Shotaro Yagishita , Masaru Ito

This paper focuses on developing a conditional gradient algorithm for multiobjective optimization problems with an unbounded feasible region. We employ the concept of recession cone to establish the well-defined nature of the algorithm. The…

Optimization and Control · Mathematics 2024-03-06 Wang Chen , Yong Zhao , Liping Tang , Xinmin Yang

We propose efficient methods for solving stochastic simple bilevel optimization problems with convex inner levels, where the goal is to minimize an outer stochastic objective function subject to the solution set of an inner stochastic…

Optimization and Control · Mathematics 2025-11-25 Khanh-Hung Giang-Tran , Soroosh Shafiee , Nam Ho-Nguyen

This paper addresses unconstrained multiobjective optimization problems where two or more continuously differentiable functions have to be minimized. We delve into the conjugate gradient methods proposed by Lucambio P\'{e}rez and Prudente…

Optimization and Control · Mathematics 2024-10-15 Wang Chen , Yong Zhao , Liping Tang , Xinmin Yang

Motivated by robust matrix recovery problems such as Robust Principal Component Analysis, we consider a general optimization problem of minimizing a smooth and strongly convex loss function applied to the sum of two blocks of variables,…

Machine Learning · Computer Science 2019-11-19 Dan Garber , Shoham Sabach , Atara Kaplan

We study convex optimization problems over a compact convex set where projections are expensive but a linear minimization oracle (LMO) is available. We propose the adaptive conditional gradient sliding method (AdCGS), a projection-free and…

Optimization and Control · Mathematics 2026-01-29 Shota Takahashi

In this paper, we propose a Newton method for unconstrained set optimization problems to find its weakly minimal solutions with respect to lower set-less ordering. The objective function of the problem under consideration is given by…

Optimization and Control · Mathematics 2024-10-01 Debdas Ghosh , Anshika , Qamrul Hasan Ansari , Xiaopeng Zhao

Recent advances in convex optimization have leveraged computer-assisted proofs to develop optimized first-order methods that improve over classical algorithms. However, each optimized method is specially tailored for a particular problem…

Optimization and Control · Mathematics 2025-07-01 Jinho Bok , Jason M. Altschuler

In this paper we consider a composite optimization problem that minimizes the sum of a weakly smooth function and a convex function with either a bounded domain or a uniformly convex structure. In particular, we first present a…

Optimization and Control · Mathematics 2023-05-30 Masaru Ito , Zhaosong Lu , Chuan He

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…

Optimization and Control · Mathematics 2013-02-14 Ion Necoara , Andrei Patrascu

Subgradient methods are the natural extension to the non-smooth case of the classical gradient descent for regular convex optimization problems. However, in general, they are characterized by slow convergence rates, and they require…

Optimization and Control · Mathematics 2023-11-20 Alessandro Scagliotti , Piero Colli Franzone

In this paper we study proximal conditional-gradient (CG) and proximal gradient-projection type algorithms for a block-structured constrained nonconvex optimization model, which arises naturally from tensor data analysis. First, we…

Optimization and Control · Mathematics 2014-10-16 Bo Jiang , Shuzhong Zhang

In this paper, we propose a proximal gradient method and an accelerated proximal gradient method for solving composite optimization problems, where the objective function is the sum of a smooth and a convex, possibly nonsmooth, function. We…

Optimization and Control · Mathematics 2025-07-22 Raghu Bollapragada , Shagun Gupta

We suggest simple implementable modifications of conditional gradient and gradient projection methods for smooth convex optimization problems in Hilbert spaces. Usually, the custom methods attain only weak convergence. We prove strong…

Optimization and Control · Mathematics 2017-05-04 Igor Konnov

We present a new feasible proximal gradient method for constrained optimization where both the objective and constraint functions are given by the summation of a smooth, possibly nonconvex function and a convex simple function. The…

Optimization and Control · Mathematics 2024-02-01 Digvijay Boob , Qi Deng , Guanghui Lan

In this paper we present a new method for solving optimization problems involving the sum of two proper, convex, lower semicontinuous functions, one of which has Lipschitz continuous gradient. The proposed method has a hybrid nature that…

Optimization and Control · Mathematics 2022-11-03 Kristian Bredies , Enis Chenchene , Alireza Hosseini