convex function – Optimization Online

Randomized Derivative-Free Optimization of Noisy Convex Functions

Published: 2015/07/13

Stochastic Programming, Unconstrained Optimization convex function, derivative-free optimization, random noisy, randomized search

We propose STARS, a randomized derivative-free algorithm for unconstrained optimization when the function evaluations are contaminated with random noise. STARS takes dynamic, noise-adjusted smoothing step-sizes that minimize the least-squares error between the true directional derivative of a noisy function and its finite difference approximation. We provide a convergence rate analysis of STARS for solving convex … Read more

The kernel average for two convex functions and its application to the extension and representation of monotone operators

Published: 2007/05/09

Heinz Bauschke

Xianfu Wang

Convex Optimization arithmetic average, autoconjugate, convex function, epigraphical average, fenchel conjugate, fitzpatrick function, monotone operator, proximal average, proximal mapping, selfdual lagrangian

We provide and analyze a based average for two convex functions, based on a kernel function. It covers several known averages such as the arithmetic average, epigraphical average, and the proximal average. When applied to the Fitzpatrick function and the conjugate of Fitzpatrick function associated with a monotone operator, our average produces an autoconjugate (also … Read more