A Robbins-Monro type algorithm for computing global minimizer of generalized conic functions

TL;DR

This paper introduces a stochastic Robbins-Monro type algorithm designed to find the global minimizer of generalized conic functions, extending previous notions and providing convergence guarantees.

Contribution

It generalizes the concept of conic functions and develops a new stochastic algorithm with proven convergence for global minimization.

Findings

Algorithm converges almost surely

Algorithm converges in L^q sense

Extends properties of conic functions

Abstract

We generalize the notion and some properties of the conic function introduced by Vincze and Nagy (2012). We provide a stochastic algorithm for computing the global minimizer of generalized conic functions, we prove almost sure and L^q-convergence of this algorithm.