Related papers: Harnessing structure in composite nonsmooth minimi…
In this work, we consider convex optimization problems with smooth objective function and nonsmooth functional constraints. We propose a new stochastic gradient algorithm, called Stochastic Halfspace Approximation Method (SHAM), to solve…
This note is concerned with the problem of minimizing a separable, convex, composite (smooth and nonsmooth) function subject to linear constraints. We study a randomized block-coordinate interpretation of the Chambolle-Pock primal-dual…
This work concerns the global minimization of a prescribed eigenvalue or a weighted sum of prescribed eigenvalues of a Hermitian matrix-valued function depending on its parameters analytically in a box. We describe how the analytical…
We show that any smooth bi-Lipschitz $h$ can be represented exactly as a composition $h_m \circ ... \circ h_1$ of functions $h_1,...,h_m$ that are close to the identity in the sense that each $\left(h_i-\mathrm{Id}\right)$ is Lipschitz, and…
Submodularity is a fundamental phenomenon in combinatorial optimization. Submodular functions occur in a variety of combinatorial settings such as coverage problems, cut problems, welfare maximization, and many more. Therefore, a lot of…
We develop a stochastic trust-region algorithm for minimizing the sum of a possibly nonconvex Lipschitz-smooth function that can only be evaluated stochastically and a nonsmooth, deterministic, convex function. This algorithm, which we call…
Submodular maximization generalizes many fundamental problems in discrete optimization, including Max-Cut in directed/undirected graphs, maximum coverage, maximum facility location and marketing over social networks. In this paper we…
Optimization of frame structures is formulated as a~non-convex optimization problem, which is currently solved to local optimality. In this contribution, we investigate four optimization approaches: (i) general non-linear optimization, (ii)…
We consider the problem of minimizing a convex, separable, nonsmooth function subject to linear constraints. The numerical method we propose is a block-coordinate extension of the Chambolle-Pock primal-dual algorithm. We prove convergence…
We propose a unifying algorithm for non-smooth non-convex optimization. The algorithm approximates the objective function by a convex model function and finds an approximate (Bregman) proximal point of the convex model. This approximate…
In this paper we provide the resolvent computation of the parallel composition of a maximally monotone operator by a linear operator under mild assumptions. Connections with a modification of the warped resolvent are provided. In the…
In this paper, a multi-parameterized proximal point algorithm combining with a relaxation step is developed for solving convex minimization problem subject to linear constraints. We show its global convergence and sublinear convergence rate…
This paper proposes and develops inexact proximal methods for finding stationary points of the sum of a smooth function and a nonsmooth weakly convex one, where an error is present in the calculation of the proximal mapping of the nonsmooth…
We introduce computable projection operators onto piecewise polynomial spaces, defined via sampling and discrete least-squares polynomial approximations. The resulting mappings exhibit (almost) optimal approximation properties in $L^2$ and…
We study composition operators on spaces of holomorphic Lipschitz functions defined on the open unit ball of a complex Banach space. Our approach is based on the linearization of the symbol through the holomorphic Lipschitz-free spaces,…
We propose an algorithm for computing the proximity operator of a sum of composite convex functions in Hilbert spaces and investigate its asymptotic behavior. Applications to best approximation and image recovery are described.
We analyze two classical algorithms for solving additively composite convex optimization problems where the objective is the sum of a smooth term and a nonsmooth regularizer: proximal stochastic gradient method for a single regularizer; and…
An algorithm is proposed, analyzed, and tested for minimizing locally Lipschitz objective functions that may be nonconvex and/or nonsmooth. The algorithm, which is built upon the gradient-sampling methodology, is designed specifically for…
We propose and analyze asymptotic proximal point (APP) methods to find the global minimizer for a class of nonconvex, nonsmooth, or even discontinuous multiple minima functions. The method is based on an asymptotic representation of…
In this paper, we address stochastic optimization problems involving a composition of a non-smooth outer function and a smooth inner function, a formulation frequently encountered in machine learning and operations research. To deal with…