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In this article, we build on previous work to present an optimization algorithm for nonlinearly constrained multi-objective optimization problems. The algorithm combines a surrogate-assisted derivative-free trust-region approach with the…

In this paper, we consider the problem of identifying a linear map from measurements which are subject to intermittent and arbitarily large errors. This is a fundamental problem in many estimation-related applications such as fault…

A regularization algorithm allowing random noise in derivatives and inexact function values is proposed for computing approximate local critical points of any order for smooth unconstrained optimization problems. For an objective function…

In this paper, we propose a proximal gradient method and an accelerated proximal gradient method for solving composite optimization problems, where the objective function is the sum of a smooth and a convex, possibly nonsmooth, function. We…

A method is proposed for solving equality constrained nonlinear optimization problems involving twice continuously differentiable functions. The method employs a trust funnel approach consisting of two phases: a first phase to locate an…

In this paper we analyze several new methods for solving nonconvex optimization problems with the objective function formed as a sum of two terms: one is nonconvex and smooth, and another is convex but simple and its structure is known.…

In this paper we propose a general algorithmic framework for first-order methods in optimization in a broad sense, including minimization problems, saddle-point problems and variational inequalities. This framework allows to obtain many…

We present new methods for solving a broad class of bound-constrained nonsmooth composite minimization problems. These methods are specially designed for objectives that are some known mapping of outputs from a computationally expensive…

In practice, optimization tasks have some structure that allows developing new algorithms for every problem with faster convergence rates. Using the structure of optimization tasks, we can propose algorithms with more optimistic convergence…

Computing the rate-distortion function for continuous sources is commonly regarded as a standard continuous optimization problem. When numerically addressing this problem, a typical approach involves discretizing the source space and…

Based on the ideas of arXiv:1710.06612, we consider the problem of minimization of the Holder-continuous non-smooth functional $f$ with non-positive convex (generally, non-smooth) Lipschitz-continuous functional constraint. We propose some…

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…

In this paper, we propose an optimization-based method for robust phase retrieval problem where the goal is to estimate an unknown signal from a quadratic measurement corrupted by outliers. To enhance the robustness of existing optimization…

We present an iterative inverse reinforcement learning algorithm to infer optimal cost functions in continuous spaces. Based on a popular maximum entropy criteria, our approach iteratively finds a weight improvement step and proposes a…

We present a flexible trust region descend algorithm for unconstrained and convexly constrained multiobjective optimization problems. It is targeted at heterogeneous and expensive problems, i.e., problems that have at least one objective…

In machine learning research, the proximal gradient methods are popular for solving various optimization problems with non-smooth regularization. Inexact proximal gradient methods are extremely important when exactly solving the proximal…

Recoverable robust optimization is a multi-stage approach, where it is possible to adjust a first-stage solution after the uncertain cost scenario is revealed. We analyze this approach for a class of selection problems. The aim is to choose…

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…

We consider the problem of optimizing the sum of a smooth, nonconvex function for which derivatives are unavailable, and a convex, nonsmooth function with easy-to-evaluate proximal operator. Of particular focus is the case where the smooth…

In this work, we consider methods for solving large-scale optimization problems with a possibly nonsmooth objective function. The key idea is to first specify a class of optimization algorithms using a generic iterative scheme involving…