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In this talk, the speaker will discuss constrained optimization. The speaker will focus on two important subclasses: bound-constrained nonconvex optimization and linear programming. Typical applications of them include nonnegative matrix factorization and optimal transport (OT) problems, which are popular topics in both mathematics and data science. To resolve the former subclass, the speaker will propose a projected Newton-CG algorithm. This algorithm is designed to possess both practicality and worst-case complexity guarantees matching the best known in literature. For the linear programming formulation of OT, the speaker will discuss random block coordinate descent (RBCD) methods. A direct advantage of these methods is to save memory. In addition, the speaker and his team’s preliminary numerical experiments show that it competes well with the classical Sinkhorn’s algorithm.
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