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We investigate routing policies for shortest path problems with uncertain arc lengths. The objective is to minimize a risk measure of the total travel time. We use the conditional value-at-risk (CVaR) for when the arc lengths (durations) have known distributions and the worst-case CVaR for when these distributions are only partially described. Policies which minimize the expected travel time (average-optimal...
Multi-stage stochastic programming provides a versatile framework for optimal decision making under uncertainty, but it gives rise to hard functional optimization problems since the adaptive recourse decisions must be modeled as functions of some or all uncertain parameters. We propose to approximate these recourse decisions by polynomial decision rules and show that the best polynomial decision rule...
Robust dynamic optimization problems involving adaptive decisions are computationally intractable in general. Tractable upper bounding approximations can be obtained by requiring the adaptive decisions to be representable as linear decision rules (LDRs). In this paper we investigate families of tractable lower bounding approximations, which serve to estimate the degree of suboptimality of the best...
We consider robust feedback control of time-varying, linear discrete-time systems operating over a finite horizon. For such systems, we consider the problem of designing robust causal controllers that minimize the expected value of a convex quadratic cost function, subject to mixed linear state and input constraints. Determination of an optimal control policy for such problems is generally computationally...
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