The recent algorithm proposed in [15] (called pcpa) for convex nonsmooth optimization, is specialized for applications in telecommunications on some nonlinear multicommodity flows problems. In this context, the objective function is additive and this property could be exploited for a better performance.

We investigate a nonconvex, nonsmooth optimization approach based on DC (Difference of Convex functions) programming and DCA (DC Algorithm) for the so-called fitting problem, which aims to fit given set data points by function. The problem is tackled as minimizing squared Euclidean norm error. It formulated program standard scheme developed. Furthermore, modified with successive decomposition p...

This paper focuses on convex constrained optimization problems, where the solution is subject to a convex inequality constraint. In particular, we aim at challenging problems for which both projection into the constrained domain and a linear optimization under the inequality constraint are time-consuming, which render both projected gradient methods and conditional gradient methods (a.k.a. the ...

This paper presents a nonsmooth optimization technique for solving a special μsynthesis control problem. Attention is focused on controller synthesis problems that involve real diagonal scalings. An academic example illustrates the synthesis algorithm and a comparison is made with the well-known DK-iteration algorithm. This paper shows that nonsmooth optimization synthesis can provide better so...

In this paper we consider a fractional optimization problem that minimizes the ratio of two quadratic functions subject to a strictly convex quadratic constraint. First using the extension of Charnes-Cooper transformation, an equivalent homogenized quadratic reformulation of the problem is given. Then we show that under certain assumptions, it can be solved to global optimality using semidefini...

Consensus optimization has received considerable attention in recent years. A number of decentralized algorithms have been proposed for convex consensus optimization. However, on consensus optimization with nonconvex objective functions, our understanding to the behavior of these algorithms is limited. When we lose convexity, we cannot hope for obtaining globally optimal solutions (though we st...

We study the extension of the Chambolle–Pock primal-dual algorithm to nonsmooth optimization problems involving nonlinear operators between function spaces. Local convergence is shown under technical conditions including metric regularity of the corresponding primal-dual optimality conditions. We also show convergence for a Nesterov-type accelerated variant provided one part of the functional i...

In this paper we study the problem of minimizing condition numbers over a compact convex subset of the cone of symmetric positive semidefinite n × n matrices. We show that the condition number is a Clarke regular strongly pseudoconvex function. We prove that a global solution of the problem can be approximated by an exact or an inexact solution of a nonsmooth convex program. This asymptotic ana...

We consider convex nonsmooth optimization problems where additional information with uncontrolled accuracy is readily available. It is often the case when the objective function is itself the output of an optimization solver, as for large-scale energy optimization problems tackled by decomposition. In this paper, we study how to incorporate the uncontrolled linearizations into (proximal and lev...

A problem of great interest in optimization is to minimize a sum of two closed, proper, and convex functions where one is smooth and the other has a computationally inexpensive proximal operator. In this paper we analyze a family of Inertial Forward-Backward Splitting (I-FBS) algorithms for solving this problem. We first apply a global Lyapunov analysis to I-FBS and prove weak convergence of th...