3,179 research outputs found
Relative Robust Portfolio Optimization
Considering mean-variance portfolio problems with uncertain model parameters, we contrast the classical absolute robust optimization approach with the relative robust approach based on a maximum regret function. Although the latter problems are NP-hard in general, we show that tractable inner and outer approximations exist in several cases that are of central interest in asset management
A distributionally robust perspective on uncertainty quantification and chance constrained programming
The objective of uncertainty quantification is to certify that a given physical, engineering or economic system satisfies multiple safety conditions with high probability. A more ambitious goal is to actively influence the system so as to guarantee and maintain its safety, a scenario which can be modeled through a chance constrained program. In this paper we assume that the parameters of the system are governed by an ambiguous distribution that is only known to belong to an ambiguity set characterized through generalized moment bounds and structural properties such as symmetry, unimodality or independence patterns. We delineate the watershed between tractability and intractability in ambiguity-averse uncertainty quantification and chance constrained programming. Using tools from distributionally robust optimization, we derive explicit conic reformulations for tractable problem classes and suggest efficiently computable conservative approximations for intractable ones
Convex Relaxations and Approximations of Chance-Constrained AC-OPF Problems
This paper deals with the impact of linear approximations for the unknown
nonconvex confidence region of chance-constrained AC optimal power flow
problems. Such approximations are required for the formulation of tractable
chance constraints. In this context, we introduce the first formulation of a
chance-constrained second-order cone (SOC) OPF. The proposed formulation
provides convergence guarantees due to its convexity, while it demonstrates
high computational efficiency. Combined with an AC feasibility recovery, it is
able to identify better solutions than chance-constrained nonconvex AC-OPF
formulations. To the best of our knowledge, this paper is the first to perform
a rigorous analysis of the AC feasibility recovery procedures for robust
SOC-OPF problems. We identify the issues that arise from the linear
approximations, and by using a reformulation of the quadratic chance
constraints, we introduce new parameters able to reshape the approximation of
the confidence region. We demonstrate our method on the IEEE 118-bus system
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