2013/06/14 by Sanjay Mehrotra, Dávid Papp, Mehrotra, Sanjay +1 · 3 citations
Decision Sciences · Economics, Econometrics and Finance · Engineering · Mathematics · #90-08 #90C15 #90C25 #90C34 #Advanced Optimization Algorithms Research #Computational Finance (q-fin.CP) #Economic and Environmental Valuation #FOS: Economics and business #FOS: Mathematics #G.1.6 #Optimization and Control (math.OC) #Portfolio Management (q-fin.PM) #Risk and Portfolio Optimization #Water resources management and optimization
paper · pdf · doi:10.48550/arxiv.1306.3437
openalex publication_date 2013/06/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We present and analyze a central cutting surface algorithm for general\nsemi-infinite convex optimization problems, and use it to develop a novel\nalgorithm for distributionally robust optimization problems in which the\nuncertainty set consists of probability distributions with given bounds on\ntheir moments. Moments of arbitrary order, as well as non-polynomial moments\ncan be included in the formulation. We show that this gives rise to a hierarchy\nof optimization problems with decreasing levels of risk-aversion, with classic\nrobust optimization at one end of the spectrum, and stochastic programming at\nthe other. Although our primary motivation is to solve distributionally robust\noptimization problems with moment uncertainty, the cutting surface method for\ngeneral semi-infinite convex programs is also of independent interest. The\nproposed method is applicable to problems with non-differentiable semi-infinite\nconstraints indexed by an infinite-dimensional index set. Examples comparing\nthe cutting surface algorithm to the central cutting plane algorithm of\nKortanek and No demonstrate the potential of our algorithm even in the solution\nof traditional semi-infinite convex programming problems whose constraints are\ndifferentiable and are indexed by an index set of low dimension. After the rate\nof convergence analysis of the cutting surface algorithm, we extend the\nauthors' moment matching scenario generation algorithm to a probabilistic\nalgorithm that finds optimal probability distributions subject to moment\nconstraints. The combination of this distribution optimization method and the\ncentral cutting surface algorithm yields a solution to a family of\ndistributionally robust optimization problems that are considerably more\ngeneral than the ones proposed to date.\n