An Augmented Lagrangian Decomposition Method for Chance-Constrained Optimization Problems

Joint chance-constrained optimization problems under discrete distributions arise frequently in financial management and business operations. These can be reformulated as mixed-integer programs. The size of integer programs is usually very large even though the original problem medium size. This paper studies an augmented Lagrangian decomposition method for finding high-quality feasible solutions complex problems, including nonconvex problems. Different from current approaches, proposed allows randomness to appear both left-hand-side matrix right-hand-side vector chance constraint. In addition, only requires solving a convex subproblem 0-1 knapsack at each iteration. Based on special structure constraint, computed quasi-linear time, which keeps computation subproblems relatively low level. convergence first-order stationary point established certain mild conditions. Numerical results are presented comparison with set existing methods literature various real-world models. It observed that compares favorably terms quality best solution obtained within time large-size particularly when objective function or constraints random.