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We study a class of optimization problems in which the objective function is given by the sum of a differentiable but possibly nonconvex component and a nondifferentiable convex regularization term. We introduce an auxiliary variable to…

Optimization and Control · Mathematics 2019-08-27 Neil K. Dhingra , Sei Zhen Khong , Mihailo R. Jovanović

This paper presents an accelerated proximal gradient method for multiobjective optimization, in which each objective function is the sum of a continuously differentiable, convex function and a closed, proper, convex function. Extending…

Optimization and Control · Mathematics 2023-06-08 Hiroki Tanabe , Ellen H. Fukuda , Nobuo Yamashita

We consider the proximal gradient method on Riemannian manifolds for functions that are possibly not geodesically convex. Starting from the forward-backward-splitting, we define an intrinsic variant of the proximal gradient method that uses…

Optimization and Control · Mathematics 2025-06-12 Ronny Bergmann , Hajg Jasa , Paula John , Max Pfeffer

We consider the problem of minimizing a finite sum of convex functions subject to the set of minimizers of a convex differentiable function. In order to solve the problem, an algorithm combining the incremental proximal gradient method with…

Optimization and Control · Mathematics 2020-04-21 Nimit Nimana , Narin Petrot

We consider the problem of minimizing a convex objective which is the sum of a smooth part, with Lipschitz continuous gradient, and a nonsmooth part. Inspired by various applications, we focus on the case when the nonsmooth part is a…

Optimization and Control · Mathematics 2013-08-28 Ting Kei Pong

Many large-scale and distributed optimization problems can be brought into a composite form in which the objective function is given by the sum of a smooth term and a nonsmooth regularizer. Such problems can be solved via a proximal…

Optimization and Control · Mathematics 2020-06-26 Sepideh Hassan-Moghaddam , Mihailo R. Jovanović

The incremental aggregated gradient algorithm is popular in network optimization and machine learning research. However, the current convergence results require the objective function to be strongly convex. And the existing convergence…

Optimization and Control · Mathematics 2019-10-14 Tao Sun , Yuejiao Sun , Dongsheng Li , Qing Liao

Extrapolation is a well-known technique for solving convex optimization and variational inequalities and recently attracts some attention for non-convex optimization. Several recent works have empirically shown its success in some machine…

Optimization and Control · Mathematics 2019-02-06 Yi Xu , Zhuoning Yuan , Sen Yang , Rong Jin , Tianbao Yang

In this paper we analyze a class of nonconvex optimization problem from the viewpoint of abstract convexity. Using the respective generalizations of the subgradient we propose an abstract notion proximal operator and derive a number of…

Optimization and Control · Mathematics 2024-02-29 Ewa Bednarczuk , Dirk Lorenz , The Hung Tran

We consider a variable metric linesearch based proximal gradient method for the minimization of the sum of a smooth, possibly nonconvex function plus a convex, possibly nonsmooth term. We prove convergence of this iterative algorithm to a…

Numerical Analysis · Mathematics 2017-04-11 Silvia Bonettini , Ignace Loris , Federica Porta , Marco Prato , Simone Rebegoldi

In this paper, we consider a broad class of nonconvex and nonsmooth optimization problems, where one objective component is a nonsmooth weakly convex function composed with a linear operator. By integrating variable smoothing techniques…

Optimization and Control · Mathematics 2025-11-03 Xian-Jun Long , Kang Zeng , Gao-Xi Li , Minh N. Dao , Zai-Yun Peng

In this paper, we consider the composite optimization problem, where the objective function integrates a continuously differentiable loss function with a nonsmooth regularization term. Moreover, only the function values for the…

Optimization and Control · Mathematics 2024-01-09 Shanglin Liu , Lei Wang , Nachuan Xiao , Xin Liu

In this paper we analyze a zeroth-order proximal stochastic gradient method suitable for the minimization of weakly convex stochastic optimization problems. We consider nonsmooth and nonlinear stochastic composite problems, for which…

Optimization and Control · Mathematics 2025-04-21 Spyridon Pougkakiotis , Dionysios S. Kalogerias

Composite minimization involves a collection of smooth functions which are aggregated in a nonsmooth manner. In the convex setting, we design an algorithm by linearizing each smooth component in accordance with its main curvature. The…

Optimization and Control · Mathematics 2019-03-26 Jérôme Bolte , Zheng Chen , Edouard Pauwels

In this paper, we propose an efficient and flexible algorithm to solve dynamic mean-field planning problems based on an accelerated proximal gradient method. Besides an easy-to-implement gradient descent step in this algorithm, a crucial…

Optimization and Control · Mathematics 2021-03-01 Jiajia Yu , Rongjie Lai , Wuchen Li , Stanley Osher

In this paper, we consider a broad class of nonsmooth and nonconvex fractional programs, where the numerator can be written as the sum of a continuously differentiable convex function whose gradient is Lipschitz continuous and a proper…

Optimization and Control · Mathematics 2022-01-19 Radu Ioan Boţ , Minh N. Dao , Guoyin Li

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

Riemannian accelerated gradient methods have been well studied for smooth optimization, typically treating geodesically convex and geodesically strongly convex cases separately. However, their extension to nonsmooth problems on manifolds…

Optimization and Control · Mathematics 2025-09-29 Shuailing Feng , Yuhang Jiang , Wen Huang , Shihui Ying

This paper investigates a category of constrained fractional optimization problems that emerge in various practical applications. The objective function for this category is characterized by the ratio of a numerator and denominator, both…

Optimization and Control · Mathematics 2026-05-28 Yizun Lin , Jian-Feng Cai , Zhao-Rong Lai , Cheng Li

The proximal point algorithm is a widely used tool for solving a variety of convex optimization problems such as finding zeros of maximally monotone operators, fixed points of nonexpansive mappings, as well as minimizing convex functions.…

Optimization and Control · Mathematics 2018-04-19 Laurentiu Leustean , Adriana Nicolae , Andrei Sipos