268 research outputs found
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
Data-Driven Chance Constrained Programs over Wasserstein Balls
We provide an exact deterministic reformulation for data-driven chance
constrained programs over Wasserstein balls. For individual chance constraints
as well as joint chance constraints with right-hand side uncertainty, our
reformulation amounts to a mixed-integer conic program. In the special case of
a Wasserstein ball with the -norm or the -norm, the cone is the
nonnegative orthant, and the chance constrained program can be reformulated as
a mixed-integer linear program. Our reformulation compares favourably to
several state-of-the-art data-driven optimization schemes in our numerical
experiments.Comment: 25 pages, 9 figure
Data-driven chance constrained programs over wasserstein balls
We provide an exact deterministic reformulation for data-driven, chance-constrained programs over Wasserstein balls. For individual chance constraints as well as joint chance constraints with right-hand-side uncertainty, our reformulation amounts to a mixed-integer conic program. In the special case of a Wasserstein ball with the 1-norm or the ∞-norm, the cone is the nonnegative orthant, and the chance-constrained program can be reformulated as a mixed-integer linear program. Our reformulation compares favorably to several state-of-the-art data-driven optimization schemes in our numerical experiments
Conic Reformulations for Kullback-Leibler Divergence Constrained Distributionally Robust Optimization and Applications
In this paper, we consider a distributionally robust optimization (DRO) model
in which the ambiguity set is defined as the set of distributions whose
Kullback-Leibler (KL) divergence to an empirical distribution is bounded.
Utilizing the fact that KL divergence is an exponential cone representable
function, we obtain the robust counterpart of the KL divergence constrained DRO
problem as a dual exponential cone constrained program under mild assumptions
on the underlying optimization problem. The resulting conic reformulation of
the original optimization problem can be directly solved by a commercial conic
programming solver. We specialize our generic formulation to two classical
optimization problems, namely, the Newsvendor Problem and the Uncapacitated
Facility Location Problem. Our computational study in an out-of-sample analysis
shows that the solutions obtained via the DRO approach yield significantly
better performance in terms of the dispersion of the cost realizations while
the central tendency deteriorates only slightly compared to the solutions
obtained by stochastic programming
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