15 papers · ranked by Valyu relevance
Gonglin Yuan, Zhou Sheng, Wenjie Liu, Hans A Kestler
In this paper, the Hager and Zhang (HZ) conjugate gradient (CG) method and the modified HZ (MHZ) CG method are presented for large-scale nonsmooth convex minimization. Under some mild conditions, convergent results of the proposed methods are established. Numerical results show that the presented methods can be better…
Yong Li, Gonglin Yuan, Zhou Sheng, Marzio Alfio Pennisi
It is well known that the active set algorithm is very effective for smooth box constrained optimization. Many achievements have been obtained in this field. We extend the active set method to nonsmooth box constrained optimization problems, using the Moreau-Yosida regularization technique to make the objective…
Zengru Cui, Gonglin Yuan, Zhou Sheng, Wenjie Liu + 3 more
'Xiabin Duan' 'Lixiang Li'] This paper proposes a modified BFGS formula using a trust region model for solving nonsmooth convex minimizations by using the Moreau-Yosida regularization (smoothing) approach and a new secant equation with a BFGS update formula. Our algorithm uses the function value information and…
Daria Ghilli, Karl Kunisch
A general class of nonconvex optimization problems is considered, where the penalty is the composition of a linear operator with a nonsmooth nonconvex mapping, which is concave on the positive real line. The necessary optimality condition of a regularized version of the original problem is solved by means of a…
Radu Ioan Boţ, Mikhail A. Karapetyants
In a Hilbert setting, we study the convergence properties of the second order in time dynamical system combining viscous and Hessian-driven damping with time scaling in relation to the minimization of a nonsmooth and convex function. The system is formulated in terms of the gradient of the Moreau envelope of the…
Yaxuan Zhang, Songnian He
In this paper, we study the minimization problem of the type \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt}…
Nadhir Ben Rached, Shyam Mohan Subbiah Pillai, Raúl Tempone, Yousri Slaoui + 1 more
'Yousri Slaoui' 'Solym Manou-Abi'] Given the increasing global emphasis on sustainable energy usage and the rising energy demands of cellular wireless networks, this work seeks an optimal short-term, continuous-time power-procurement schedule to minimize operating expenditure and the carbon footprint of cellular…
Liping Feng, Liang Ran, Guoyang Meng, Jialong Tang + 3 more
'Huaqing Li' 'Shu-Chuan Chu'] In this paper, we focus on the nonsmooth composite optimization problems over networks, which consist of a smooth term and a nonsmooth term. Both equality constraints and box constraints for the decision variables are also considered. Based on the multi-agent networks, the objective…
Axel Böhm, Stephen J. Wright
We study minimization of a structured objective function, being the sum of a smooth function and a composition of a weakly convex function with a linear operator. Applications include image reconstruction problems with regularizers that introduce less bias than the standard convex regularizers. We develop a variable…
Ke Su, Shaohua Liu, Wei Lu, Fei Chen
In this paper, we proposed an adaptive QP-free method without a penalty function or a filter for minimax optimization. In each iteration, solved two linear systems of equations constructed from Lagrange multipliers and KKT-conditioned NCP functions. Based on the work set, the computational scale is further reduced.…
Radu Ioan Boţ, Axel Böhm
We investigate the convergence properties of incremental mirror descent type subgradient algorithms for minimizing the sum of convex functions. In each step, we only evaluate the subgradient of a single component function and mirror it back to the feasible domain, which makes iterations very cheap to compute. The…
Caroline Geiersbach, Teresa Scarinci
For finite-dimensional problems, stochastic approximation methods have long been used to solve stochastic optimization problems. Their application to infinite-dimensional problems is less understood, particularly for nonconvex objectives. This paper presents convergence results for the stochastic proximal gradient…
Sandy Bitterlich, Radu Ioan Boţ, Ernö Robert Csetnek, Gert Wanka
The Alternating Minimization Algorithm has been proposed by Paul Tseng to solve convex programming problems with two-block separable linear constraints and objectives, whereby (at least) one of the components of the latter is assumed to be strongly convex. The fact that one of the subproblems to be solved within the…
Shouqiang Du, Miao Chen
\usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$l_{1}$\end{document} l 1 -norm minimization problem Authors: ['Shouqiang Du' 'Miao Chen'] We consider a kind of nonsmooth…
Mohammad Dehghani, Štěpán Hubálovský, Pavel Trojovský, Wojciech Kempa + 1 more
'Wojciech Kempa' 'Iwona Paprocka'] Numerous optimization problems designed in different branches of science and the real world must be solved using appropriate techniques. Population-based optimization algorithms are some of the most important and practical techniques for solving optimization problems. In this paper, a…