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We consider a separation problem where the observation consists of the sum of a high amplitude smooth signal and a low amplitude transient signal. We propose a method for decomposition that relies on solving instances of a `constrained…
In this paper, we first study nonsmooth steepest descent method for nonsmooth functions defined on Hilbert space and establish the corresponding algorithm by proximal subgradients. Then, we use this algorithm to find stationary points for…
The task of recovering a low-rank matrix from its noisy linear measurements plays a central role in computational science. Smooth formulations of the problem often exhibit an undesirable phenomenon: the condition number, classically…
This work proposes an implementable proximal-type method for a broad class of optimization problems involving nonsmooth and nonconvex objective and constraint functions. In contrast to existing methods that rely on an ad hoc model…
This paper proposes several novel optimization algorithms for minimizing a nonlinear objective function. The algorithms are enlightened by the optimal state trajectory of an optimal control problem closely related to the minimized objective…
We develop a new optimisation technique that combines multiresolution subdivision surfaces for boundary description with immersed finite elements for the discretisation of the primal and adjoint problems of optimisation. Similar to wavelets…
This book is devoted to finite-dimensional problems of non-convex non-smooth optimization and numerical methods for their solution. The problem of nonconvexity is studied in the book on two main models of nonconvex dependencies: these are…
This paper bridges discrete and continuous optimization approaches for decomposable submodular function minimization, in both the standard and parametric settings. We provide improved running times for this problem by reducing it to a…
The article introduces a new algorithm for solving a class ofequilibrium problems involving strongly pseudomonotone bifunctions with Lipschitz-type condition. We describe how to incorporate the proximal-like regularized technique with…
Binary optimization is a powerful tool for modeling combinatorial problems, yet scalable and theoretically sound solution methods remain elusive. Conventional solvers often rely on heuristic strategies with weak guarantees or struggle with…
In this paper, we consider a class of structured nonconvex nonsmooth optimization problems, in which the objective function is formed by the sum of a possibly nonsmooth nonconvex function and a differentiable function whose gradient is…
This note studies numerical methods for solving compositional optimization problems, where the inner function is smooth, and the outer function is Lipschitz continuous, non-smooth, and non-convex but exhibits one of two special structures…
In this paper, we consider the nonsmooth convex optimization problems over the fixed point constraint sets of firmly nonexpansive operators. To find an optimal solution of the problem, we present an iterative method based on the hybrid…
In this paper, we consider two types of problems that have some similarity in their structure, namely, min-min problems and min-max saddle-point problems. Our approach is based on considering the outer minimization problem as a minimization…
Submodular functions describe a variety of discrete problems in machine learning, signal processing, and computer vision. However, minimizing submodular functions poses a number of algorithmic challenges. Recent work introduced an…
This paper presents a lower bound for optimizing a finite sum of $n$ functions, where each function is $L$-smooth and the sum is $\mu$-strongly convex. We show that no algorithm can reach an error $\epsilon$ in minimizing all functions from…
We study the problem of zero-order optimization of a strongly convex function. The goal is to find the minimizer of the function by a sequential exploration of its values, under measurement noise. We study the impact of higher order…
We study a non-parametric multi-armed bandit problem with stochastic covariates, where a key complexity driver is the smoothness of payoff functions with respect to covariates. Previous studies have focused on deriving minimax-optimal…
This paper develops high-accuracy methods for numerically solving optimal control problems subject to nonsmooth differential equations with set-valued step functions. A notable subclass of these systems are Filippov systems. The set-valued…
We consider the problem of maximizing non-negative non-decreasing set functions. Although most of the recent work focus on exploiting submodularity, it turns out that several objectives we encounter in practice are not submodular.…