Model Construction for Convex-Constrained Derivative-Free Optimization

2024/03/22 by Lindon Roberts, Roberts, Lindon · 2 citations
Computer Science · Engineering · #Advanced Control Systems Optimization #FOS: Mathematics #Optimization and Control (math.OC) #Robotic Path Planning Algorithms

paper · pdf · doi:10.48550/arxiv.2403.14960

openalex publication_date 2024/03/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We develop a new approximation theory for linear and quadratic interpolation models, suitable for use in convex-constrained derivative-free optimization (DFO). Most existing model-based DFO methods for constrained problems assume the ability to construct sufficiently accurate approximations via interpolation, but the standard notions of accuracy (designed for unconstrained problems) may not be achievable by only sampling feasible points, and so may not give practical algorithms. This work extends the theory of convex-constrained linear interpolation developed in [Hough & Roberts, SIAM J. Optim, 32:4 (2022), pp. 2552-2579] to the case of linear regression models and underdetermined quadratic interpolation models.

Cited by

• A derivative-free trust-region approach for Low Order-Value Optimization problems
• CLARSTA: A random subspace trust-region algorithm for convex-constrained derivative-free optimization

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