2016/12/15 by Warren Hare, Hare, Warren
Computer Science · Engineering · Mathematics · #Advanced Optimization Algorithms Research #FOS: Mathematics #Numerical Analysis (math.NA) #Optimization and Variational Analysis #Sparse and Compressive Sensing Techniques
paper · pdf · doi:10.48550/arxiv.1612.05190
openalex publication_date 2016/12/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Derivative-free optimization (DFO) is the mathematical study of the optimization algorithms that do not use derivatives. One branch of DFO focuses on model-based DFO methods, where an approximation of the objective function is used to guide the optimization algorithm. Proving convergence of such methods often applies an assumption that the approximations form \em fully linear models -- an assumption that requires the true objective function to be smooth. However, some recent methods have loosened this assumption and instead worked with functions that are compositions of smooth functions with simple convex functions (the max-function or the ℓ1 norm). In this paper, we examine the error bounds resulting from the composition of a convex lower semi-continuous function with a smooth vector-valued function when it is possible to provide fully linear models for each component of the vector-valued function. We derive error bounds for the resulting function values and subgradient vectors.