Model-Based Derivative-Free Methods for Convex-Constrained Optimization

Matthew Hough; Lindon Roberts

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arXiv · 2111.05443

Model-Based Derivative-Free Methods for Convex-Constrained Optimization

Matthew Hough·Lindon Roberts

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Abstract

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 and a worst-case complexity of $O(\epsilon^{-2})$ iterations and objective evaluations for nonconvex functions, matching results for the unconstrained case. We introduce new, weaker requirements on model accuracy compared to existing methods. As a result, sufficiently accurate interpolation models can be constructed only using feasible points. We develop a comprehensive theory of interpolation set management in this regime for linear and composite linear models. We implement our approach for nonlinear least-squares problems and demonstrate strong practical performance compared to general-purpose solvers.

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BibTeX RIS

Matthew Hough, Lindon Roberts. 2021-11-09. Model-Based Derivative-Free Methods for Convex-Constrained Optimization. https://arxiv.org/abs/2111.05443

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