Multistage Stochastic Programming with Recourse As Mathematical Programming in an $L_p $ Space

Paul Olsen

28 citations0/0 files storedSIAM Journal on Control and Optimization

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Risk and Portfolio Optimization Advanced Control Systems Optimization Advanced Optimization Algorithms Research

Abstract

Multistage stochastic programming with recourse has been formulated in terms of a recursive sequence of parameterized, finite-dimensional mathematical programming problems. It has also been formulated as mathematical programming in an $L_p $-space. The two formulations are reconciled by showing that the $L_p $-space, or static, formulation is a restriction of the recursive, or dynamic, formulation and by deriving conditions under which any solution to the static formulation solves the dynamic formulation.

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1955Linear Programming under Uncertainty 1967Stochastic Programs with Recourse 1966Programming Under Uncertainty: The Equivalent Convex Program 1966Programming Under Uncertainty: The Solution Set 1975Duality for Stochastic Programming Interpreted as L. P. in $L_p $-Space 1976Discretizations of multistage stochastic programming problems 1976Multistage Stochastic Programming with Recourse: The Equivalent Deterministic Problem 1974Continuous versus measurable recourse in N-stage stochastic programming

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