In this paper, we consider a nonsmooth convex finite-sum problem with conic constraint. To overcome the challenge of projecting onto constraint set and computing full (sub)gradient, introduce primal-dual incremental gradient scheme where only component function two constraints are used to update each sub-iteration in cyclic order. We demonstrate an asymptotic sublinear rate convergence terms su...

We develop a second order primal-dual method for optimization problems in which the objective function is given by sum of strongly convex twice differentiable term and possibly nondifferentiable regularizer. After introducing an auxiliary variable, we utilize proximal operator nonsmooth regularizer to transform associated augmented Lagrangian into that once, but not twice, continuously differen...

The paper proposes and justifies a new algorithm of the proximal Newton type to solve broad class nonsmooth composite convex optimization problems without strong convexity assumptions. Based on advanced notions techniques variational analysis, we establish implementable results global convergence proposed as well its local with superlinear quadratic rates. For certain structured problems, obtai...

This monograph is about a class of optimization algorithms called proximal algorithms. Much like Newton’s method is a standard tool for solving unconstrained smooth optimization problems of modest size, proximal algorithms can be viewed as an analogous tool for nonsmooth, constrained, large-scale, or distributed versions of these problems. They are very generally applicable, but are especially ...

Abstract Currently, few approaches are available for mixed-integer nonlinear robust optimization. Those that do exist typically either require restrictive assumptions on the problem structure or not guarantee protection. In this work, we develop an algorithm convex optimization problems where a key feature is method does rely specific of inner worst-case (adversarial) and allows latter to be no...

Abstract Many practical problems, such as computer science, communications network, product design, system control, statistics and finance, etc.,can be formulated a probabilistic constrained optimization problem (PCOP) which is challenging to solve since it usually nonconvex nonsmooth. Effective methods for the mostly focus on approximation techniques, convex approximation, D.C. (difference of ...

This paper considers the image recovery problem by taking group sparsity into account as prior knowledge. is formulated a sparse optimization over intersection of polyhedron and possibly degenerate ellipsoid. It convexly constrained with cardinality objective function. We use capped folded concave function to approximate show that solution set continuous approximation solutions are same. Moreov...