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In this paper, we show the optimality of a certain class of disturbance-affine control policies in the context of one-dimensional, constrained, multi-stage robust optimization. Our results cover the finite horizon case, with minimax (worst-case) objective, and convex state costs plus linear control costs. We develop a new proof methodology, which explores(More)
This paper formalizes and adapts the well known concept of Pareto efficiency in the context of the popular robust optimization (RO) methodology. We argue that the classical RO paradigm need not produce solutions that possess the associated property of Pareto optimality, and illustrate via examples how this could lead to inefficiencies and sub-optimal(More)
In this paper, we propose a new tractable framework for dealing with multi-stage decision problems affected by uncertainty, applicable to robust optimization and stochastic programming. We introduce a hierarchy of polynomial disturbance-feedback control policies, and show how these can be computed by solving a single semidefinite programming problem. The(More)
This paper compares two different frameworks recently introduced in the literature for measuring risk in a multi-period setting. The first corresponds to applying a single coherent risk measure to the cumulative future costs, while the second involves applying a composition of one-step coherent risk mappings. We summarize the relative strengths of the two(More)
The MIT Faculty has made this article openly available. Please share how this access benefits you. Your story matters. Abstract In this paper, we propose a new tractable framework for dealing with linear dynamical systems affected by uncertainty, applicable to multi-stage robust optimization and stochastic programming. We introduce a hierarchy of(More)
CONTEXT Bone marrow (BM) examination is part of the staging workup of lymphoma patients. Few studies have compared BM histologic findings with results of flow cytometric immunophenotyping analysis in follicular lymphoma (FL) patients. OBJECTIVE To correlate histologic findings with immunophenotypic data in staging BM biopsy and aspiration specimens of FL(More)
This paper considers a particular class of dynamic robust optimization problems, where a large number of decisions must be made in the first stage, which consequently fix the constraints and cost structure underlying a one-dimensional, linear dynamical system. We seek to bridge two classical paradigms for solving such problems, namely, (1) dynamic(More)
A proper framework for measuring and mitigating risk in dynamic settings is of utmost importance, on both a practical, as well as a theoretical level. In recent years, coherent risk measures have emerged as a viable alternative to classical frameworks involving expected utility theory; their properties and axiomatic representation theorems are well(More)
We study sourcing in a supply chain with three levels: a manufacturer, Tier 1 suppliers, and Tier 2 suppliers prone to disruption from, e.g., natural disasters like earthquakes or floods. The manufacturer may not directly dictate which Tier 2 suppliers are used, but may influence the sourcing decisions of Tier 1 suppliers via contract parameters. The(More)
W e develop a new local search algorithm for binary optimization problems, whose complexity and performance are explicitly controlled by a parameter Q, measuring the depth of the local search neighborhood. We show that the algorithm is pseudo-polynomial for general cost vector c, and achieves a w 2 //2w − 1 approximation guarantee for set packing problems(More)