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02/02/06 Colloquium
Dr. Hongchao Zhang
University of Florida
University of Florida
Recent Advances in Box Constrained Optimization
Abstract: Solving large scale box constrained optimization problem efficiently is very important in both theories and many applications. This this talk, A new active set algorithm (ASA) is introduced for box constrained optimization which consists of a nonmonotone gradient projection step, an unconstrained optimization step and a set of rules for branching between these two steps. Global convergence to a stationary point is established. This algorithm eventually reduces to unconstrained optimization even without assuming the strict complementarity condtion. A specific implementation of ASA is given which exploits the recently developed cyclic Barzilai-Borwein algorithm for the gradient projection step and the recently developed conjugate gradient algorithm CG\_DESCENT for unconstrained optimization. Extensive numerical results are provided.