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
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
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 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
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 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
We present a novel accelerated primal-dual (APD) method for solving a class of deterministic and stochastic saddle point problems (SPP). The basic idea of this algorithm is to incorporate a multi-step acceleration scheme into the primal-dual method without smoothing the objective function. For deterministic SPP, the APD method achieves the same optimal rate of convergence … Read more
We further investigate the uniform regularity property of collections of sets via primal and dual characterizing constants. These constants play an important role in determining convergence rates of projection algorithms for solving feasibility problems. CitationPublished in Serdica Math. J. 39, 287–312 (2013) http://www.math.bas.bg/serdica/2013/2013-287-312.pdfArticleDownload View PDF
The $pq$-relaxation for the pooling problem can be constructed by applying McCormick envelopes for each of the bilinear terms appearing in the so-called $pq$-formulation of the pooling problem. This relaxation can be strengthened by using piecewise-linear functions that over- and under-estimate each bilinear term. The resulting relaxation can be written as a mixed integer linear … Read more
This research presents a very efficient method of solving a broad class of large-scale capacitated resource management problems by introducing a new formulation and decomposition. A heuristic called Likelihood of Assignment is utilized not only to find high quality initial integer feasible solutions, but also to guide the Branch-and-Price (B&P) Algorithm towards stabilization. Although Column … Read more