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Center for Nonlinear Studies |
Mixed-Integer Non-Convex Optimization problems have received extensive attention due to their wide applications in artificial intelligence, hybrid control, and graph theory, just to name a few. We propose first-order algorithms based on the inexact augmented Lagrangian method to solve the aforementioned problems in their original formulation as well as in equivalent reformulations. The proposed algorithms can also solve a convex Semidefinite Relaxation (SDR) of an originals NP-hard problem to gain scalability by dropping convexity. Additionally, recent work suggests that by solving the SDR with our method, each local optimum found is, under some circumstances, also a global optimum with high probability. Despite the nonconvex nature, we prove that the algorithm globally converges to a stationary point in all of the formulations, under mild assumptions. To demonstrate the scalability of our algorithms, we discuss comparative results from applying it to community detection, graph module detection, image segmentation, integrated task and motion planning for robots, and for weighted network design with cardinality constraints. Short bio: Chuangchuang Sun is currently working towards the Ph.D. degree in the Mechanical and Aerospace Engineering Department at The Ohio State University, Columbus, OH. His research interests include convex optimization, mixed-integer programming, system control and artificial intelligence. He has published more than ten technical papers in such areas.
Host: Carleton Coffrin