an:07212396
Zbl 1443.90331
Hare, Warren; Planiden, Chayne; Sagastiz??bal, Claudia
A derivative-free \(\mathcal{V} \mathcal{U}\)-algorithm for convex finite-max problems
EN
Optim. Methods Softw. 35, No. 3, 521-559 (2020).
00450031
2020
j
90C56 65K10 90C20
convex minimization; derivative-free optimization; finite-max function; proximal-point mapping; \(\mathcal{U}\)-gradient; \(\mathcal{U}\)-Hessian; \(\mathcal{V} \mathcal{U}\)-algorithm; \(\mathcal{V} \mathcal{U}\)-decomposition
This paper presents a complete and fully-functional derivative-free optimization (DFO )\(\mathcal{V}\mathcal{U}\)-algorithm for minimizing nonsmooth convex finite-max objective functions on \(R^n\) under reasonable assumptions. This algorithm is the derivative-free setting, where exact function values are available but approximations of subgradients are sufficient for convergence. Global convergence is proved. Numerical results show that, at the expence of increased CPU time and number of function calls, the DFO \(\mathcal{V}\mathcal{U}\)-algorithm gives an improvement on final function value accuracy when compared to other inexact methods, and even compared to the ExBun method that uses exact first-order information.
Nada Djuranovi??-Mili??i?? (Beograd)