Kusuoka representations provide an important and useful characterization of law invariant coherent risk measures in atomless probability spaces. However, the applicability of these results is limited by the fact that such representations do not always exist in probability spaces with atoms, such as finite probability spaces. We introduce the class of functionally coherent risk measures, … Read more
In this paper, we study distributional robust optimization approaches for a one stage stochastic minimization problem, where the true distribution of the underlying random variables is unknown but it is possible to construct a set of probability distributions which contains the true distribution and optimal decision is taken on the basis of worst possible distribution … Read more
We investigate constrained first order techniques for training Support Vector Machines (SVM) for online classification tasks. The methods exploit the structure of the SVM training problem and combine ideas of incremental gradient technique, gradient acceleration and successive simple calculations of Lagrange multipliers. Both primal and dual formulations are studied and compared. Experiments show that the … Read more
We propose a sequential quadratic optimization method for solving nonlinear optimization problems with equality and inequality constraints. The novel feature of the algorithm is that, during each iteration, the primal-dual search direction is allowed to be an inexact solution of a given quadratic optimization subproblem. We present a set of generic, loose conditions that the … Read more
This paper is on practical solutions to the multi-objective optimization problem; it advocates for single-point solutions either of the Nash equilibrium or the Tchebycheff compromise type, depending on whether one can reasonably ascribe competition or cooperation to the problem at hand. A transform method that greatly simplifies implementation of the compromise solution is presented and … Read more
We investigate the control of constrained stochastic linear systems when faced with only limited information regarding the disturbance process, i.e. when only the first two moments of the disturbance distribution are known. We consider two types of distributionally robust constraints. The constraints of the first type are required to hold with a given probability for … Read more