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This paper introduces a novel approach to system identification for nonlinear input-output models that minimizes the simulation error and frames the problem as a constrained optimization task. The proposed method addresses vanishing…
A stochastic-gradient-based interior-point algorithm for minimizing a continuously differentiable objective function (that may be nonconvex) subject to bound constraints is presented, analyzed, and demonstrated through experimental results.…
In this paper, we suggest a new framework for analyzing primal subgradient methods for nonsmooth convex optimization problems. We show that the classical step-size rules, based on normalization of subgradient, or on the knowledge of optimal…
Non-convex optimization plays a key role in a growing number of machine learning applications. This motivates the identification of specialized structure that enables sharper theoretical analysis. One such identified structure is…
Several approaches exist to model gravitational lens systems. In this study, we apply global optimization methods to find the optimal set of lens parameters using a genetic algorithm. We treat the full optimization procedure as a two-step…
We focus on a class of non-smooth optimization problems over the Stiefel manifold in the decentralized setting, where a connected network of $n$ agents cooperatively minimize a finite-sum objective function with each component being weakly…
For a model convection-diffusion problem, we address the presence of oscillatory discrete solutions, and study difficulties in recovering standard approximation results for its solution. We justify the presence of non-physical oscillations…
Composite optimization problems involve minimizing the composition of a smooth map with a convex function. Such objectives arise in numerous data science and signal processing applications, including phase retrieval, blind deconvolution,…
This paper studies the distributed optimization problem with possibly nonidentical local constraints, where its global objective function is composed of $N$ convex functions. The aim is to solve the considered optimization problem in a…
In this paper, we propose three approaches for the estimation of the Tucker decomposition of multi-way arrays (tensors) from partial observations. All approaches are formulated as convex minimization problems. Therefore, the minimum is…
Distributed optimization utilizes local computation and communication to realize a global aim of optimizing the sum of local objective functions. This article addresses a class of constrained distributed nonconvex optimization problems…
The motivation for this paper stems from the desire to develop an adaptive sampling method for solving constrained optimization problems in which the objective function is stochastic and the constraints are deterministic. The method…
In this paper we present deflation and augmentation techniques that have been designed to accelerate the convergence of Krylov subspace methods for the solution of linear systems of equations. We review numerical approaches both for linear…
An optimization algorithm for nonsmooth nonconvex constrained optimization problems with upper-C2 objective functions is proposed and analyzed. Upper-C2 is a weakly concave property that exists in difference of convex (DC) functions and…
We study the approximation of general multiobjective optimization problems with the help of scalarizations. Existing results state that multiobjective minimization problems can be approximated well by norm-based scalarizations. However, for…
The recently developed Distributed Block Proximal Method, for solving stochastic big-data convex optimization problems, is studied in this paper under the assumption of constant stepsizes and strongly convex (possibly non-smooth) local…
The problem of finding global minima of nonlinear discrete functions arises in many fields of practical matters. In recent years, methods based on discrete filled functions become popular as ways of solving these sort of problems. However,…
Nonconvex optimization problems arise in many areas of computational science and engineering and are (approximately) solved by a variety of algorithms. Existing algorithms usually only have local convergence or subsequence convergence of…
Combinatorial optimization problems can be mapped onto Ising models, and their ground state is generally difficult to find. A lot of heuristics for these problems have been proposed, and one promising approach is to use continuous…
Approximations of optimization problems arise in computational procedures and sensitivity analysis. The resulting effect on solutions can be significant, with even small approximations of components of a problem translating into large…