2019/12/26 by Vincent Guigues, Guigues, Vincent, Renato Monteiro +1
Economics, Econometrics and Finance · Decision Sciences · #Economic and Environmental Valuation #Risk and Portfolio Optimization #Auction Theory and Applications
paper · pdf · doi:10.48550/arxiv.1912.11946
We introduce StoDCuP (Stochastic Dynamic Cutting Plane), an extension of the\nStochastic Dual Dynamic Programming (SDDP) algorithm to solve multistage\nstochastic convex optimization problems. At each iteration, the algorithm\nbuilds lower affine functions not only for the cost-to-go functions, as SDDP\ndoes, but also for some or all nonlinear cost and constraint functions. We show\nthe almost sure convergence of StoDCuP. We also introduce an inexact variant of\nStoDCuP where all subproblems are solved approximately (with bounded errors)\nand show the almost sure convergence of this variant for vanishing errors.\n