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We present a model-based derivative-free method for optimization subject to general convex constraints, which we assume are unrelaxable and accessed only through a projection operator that is cheap to evaluate. We prove global convergence…

Optimization and Control · Mathematics 2022-03-18 Matthew Hough , Lindon Roberts

This paper studies the numerical solution of strictly convex unconstrained optimization problems by linesearch Newton-CG methods. We focus on methods employing inexact evaluations of the objective function and inexact and possibly random…

Optimization and Control · Mathematics 2022-05-16 Stefania Bellavia , Eugenio Fabrizi , Benedetta Morini

In this paper, we analyze a derivative-free line search method designed for bound-constrained problems. Our analysis demonstrates that this method exhibits a worst-case complexity comparable to other derivative-free methods for…

Optimization and Control · Mathematics 2025-10-29 Andrea Brilli , Andrea Cristofari , Giampaolo Liuzzi , Stefano Lucidi

In this work, we study optimization specified only through a comparison oracle: given two points, it reports which one is preferred. We call it function-free optimization because we do not assume access to, nor the existence of, a canonical…

Optimization and Control · Mathematics 2026-05-20 Katya Scheinberg , Zikai Xiong

Structured optimization problems are ubiquitous in fields like data science and engineering. The goal in structured optimization is using a prescribed set of points, called atoms, to build up a solution that minimizes or maximizes a given…

Optimization and Control · Mathematics 2021-01-14 Andrea Cristofari , Francesco Rinaldi

In this paper, we present a novel derivative-free optimization framework for solving unconstrained stochastic optimization problems. Many problems in fields ranging from simulation optimization to reinforcement learning involve settings…

Optimization and Control · Mathematics 2024-04-19 Raghu Bollapragada , Cem Karamanli , Stefan M. Wild

This paper is devoted to solving a convex stochastic optimization problem in a overparameterization setup for the case where the original gradient computation is not available, but an objective function value can be computed. For this class…

Optimization and Control · Mathematics 2024-02-14 Aleksandr Lobanov , Alexander Gasnikov

A new algorithm for smooth constrained optimization is proposed that never computes the value of the problem's objective function and that handles both equality and inequality constraints. The algorithm uses an adaptive switching strategy…

Optimization and Control · Mathematics 2026-02-13 S. Bellavia , S. Gratton , B. Morini , Ph. L. Toint

In this paper, we propose a class of penalty methods with stochastic approximation for solving stochastic nonlinear programming problems. We assume that only noisy gradients or function values of the objective function are available via…

Optimization and Control · Mathematics 2016-05-20 Xiao Wang , Shiqian Ma , Ya-xiang Yuan

We study derivative-free methods for policy optimization over the class of linear policies. We focus on characterizing the convergence rate of these methods when applied to linear-quadratic systems, and study various settings of driving…

Machine Learning · Computer Science 2020-05-19 Dhruv Malik , Ashwin Pananjady , Kush Bhatia , Koulik Khamaru , Peter L. Bartlett , Martin J. Wainwright

Zeroth-order optimization, which does not use derivative information, is one of the significant research areas in the field of mathematical optimization and machine learning. Although various studies have explored zeroth-order algorithms,…

Optimization and Control · Mathematics 2024-07-16 Ryota Nozawa , Pierre-Louis Poirion , Akiko Takeda

In this paper, we consider the problem of black box continuous submodular maximization where we only have access to the function values and no information about the derivatives is provided. For a monotone and continuous DR-submodular…

Machine Learning · Computer Science 2020-03-03 Lin Chen , Mingrui Zhang , Hamed Hassani , Amin Karbasi

We present a novel gradient-free algorithm to solve a convex stochastic optimization problem, such as those encountered in medicine, physics, and machine learning (e.g., adversarial multi-armed bandit problem), where the objective function…

Optimization and Control · Mathematics 2024-11-22 Georgii Bychkov , Darina Dvinskikh , Anastasia Antsiferova , Alexander Gasnikov , Aleksandr Lobanov

Gradient-free/zeroth-order methods for black-box convex optimization have been extensively studied in the last decade with the main focus on oracle calls complexity. In this paper, besides the oracle complexity, we focus also on iteration…

The goal of this paper is to investigate an approach for derivative-free optimization that has not received sufficient attention in the literature and is yet one of the simplest to implement and parallelize. It consists of computing…

Optimization and Control · Mathematics 2021-02-22 Hao-Jun Michael Shi , Melody Qiming Xuan , Figen Oztoprak , Jorge Nocedal

Derivative-free - or zeroth-order - optimization (DFO) has gained recent attention for its ability to solve problems in a variety of application areas, including machine learning, particularly involving objectives which are stochastic…

Optimization and Control · Mathematics 2020-08-04 Coralia Cartis , Tyler Ferguson , Lindon Roberts

Functionally constrained stochastic optimization problems, where neither the objective function nor the constraint functions are analytically available, arise frequently in machine learning applications. In this work, assuming we only have…

Optimization and Control · Mathematics 2022-10-11 Anthony Nguyen , Krishnakumar Balasubramanian

Consensus based optimization is a derivative-free particles-based method for the solution of global optimization problems. Several versions of the method have been proposed in the literature, and different convergence results have been…

Optimization and Control · Mathematics 2025-04-04 Stefania Bellavia , Greta Malaspina

In derivative-free and blackbox optimization, the objective function is often evaluated through the execution of a computer program seen as a blackbox. It can be noisy, in the sense that its outputs are contaminated by random errors.…

Optimization and Control · Mathematics 2019-11-15 Stéphane Alarie , Charles Audet , Pierre-Yves Bouchet , Sébastien Le Digabel

This work considers stochastic optimization problems in which the objective function values can only be computed by a blackbox corrupted by some random noise following an unknown distribution. The proposed method is based on sequential…

Optimization and Control · Mathematics 2023-08-15 Charles Audet , Jean Bigeon , Romain Couderc , Michael Kokkolaras