joint work with Kyle Cooper, Kalyani Nagaraj
We propose the Retrospective Partitioned Epsilon-constraint with Relaxed Local Enumeration (R-PERLE) algorithm to solve the bi-objective simulation optimization problem on integer lattices. R-PERLE is designed for simulation efficiency and provably converges to a local efficient set w.p.1 under appropriate regularity conditions. It uses a retrospective approximation (RA) framework and solves each resulting bi-objective sample-path problem only to an error tolerance commensurate with the sampling error. We discuss the design principles that make our algorithm efficient.
joint work with Stefano Lucidi, Francesco Rinaldi
A global optimization approach for solving non-monotone equilibrium problems (EPs) is proposed. The regularized gap functions are used to reformulate any EP as a constrained global optimization program and some bounds on the Lipschitz constant of such functions are provided. The proposed approach combines exact penalty functions with an improved version of the DIRECT algorithm which exploits local bounds of the Lipschitz constant. Unlike most existing methods, no monotonicity condition is assumed. Preliminary numerical results on several classes of EPs show the effectiveness of the approach.
joint work with Alexander Gasnikov, Eduard Gorbunov, Pavel Dvurechensky
We propose new accelerated stochastic gradient-free methods for convex and strongly convex optimization problems with small additive noise of unknown nature. We try to make the analysis accurate to obtain the best possible estimates on how this noise accumulates. Note that we don't assume that we "live" in a bounded set. Since that we have to show that generated sequence of points will be bounded. This requires new technique.