An outer-approximation algorithm for a class of mixed-integer nonlinear programs
Mathematical Programming: Series A and B
Mathematical Programming: Series A and B
Solving mixed integer nonlinear programs by outer approximation
Mathematical Programming: Series A and B
Discrete Time Control Problems Using MATLAB
Discrete Time Control Problems Using MATLAB
Convex Optimization
A polyhedral branch-and-cut approach to global optimization
Mathematical Programming: Series A and B
Hedging risks with interruptible load programs for a load serving entity
Decision Support Systems
A New Alternating Minimization Algorithm for Total Variation Image Reconstruction
SIAM Journal on Imaging Sciences
Fast image recovery using variable splitting and constrained optimization
IEEE Transactions on Image Processing
Foundations and Trends® in Machine Learning
An algorithmic framework for convex mixed integer nonlinear programs
Discrete Optimization
Lagrangian Duality and Branch-and-Bound Algorithms for Optimal Power Flow
Operations Research
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We propose a two-stage stochastic version of the classical economic dispatch problem with alternating-current power flow constraints, a nonconvex optimization formulation that is central to power transmission and distribution over an electricity grid. Certain generation decisions made in the first stage cannot further be changed in the second stage, where the uncertainty due to various factors such as renewable generation is realized. Any supply-demand mismatch in the second stage must be alleviated using high marginal cost power sources that can be tapped in short order. We solve a Sample-Average Approximation (SAA) of this formulation by capturing the uncertainty using a finite number of scenario samples. We propose two outer approximation algorithms to solve this nonconvex program to global optimality. We use recently discovered structural properties for the classical deterministic problem to show that when these properties hold the sequence of approximate solutions obtained under both alternatives has a limit point that is a globally optimal solution to the two-stage nonconvex SAA program. We also present an alternate local optimization approach to solving the SAA problem based on the Alternating Direction Method of Multipliers (ADMM). Numerical experiments for a variety of parameter settings were carried out to demonstrate the efficiency and usability of our method over ADMM for large practical instances.