2016/06/02 by William W. Hager, Hongchao Zhang · 30 citations
Computer Science · Engineering · Mathematics · #Advanced Optimization Algorithms Research #Algorithm #Combinatorics #Computer science #Convergence (economics) #Geometry #Mathematical optimization #Mathematics #Nonlinear programming #Nonlinear system #Optimization and Variational Analysis #Point (geometry) #Polyhedron #Projection (relational algebra) #Set (abstract data type) #Sparse and Compressive Sensing Techniques #math.OC
paper · pdf · doi:10.1007/s11425-016-0300-6
published in Science China Mathematics 59(8), 1525-1542 (Springer Nature)
openalex publication_date 2016/06/02 · arxiv created 2016/06/07 · arxiv updated 2016/06/08 · openalex created_date 2020/11/23 · openalex updated_date 2026/08/05
A polyhedral active set algorithm PASA is developed for solving a nonlinear optimization problem whose feasible set is a polyhedron. Phase one of the algorithm is the gradient projection method, while phase two is any algorithm for solving a linearly constrained optimization problem. Rules are provided for branching between the two phases. Global convergence to a stationary point is established, while asymptotically PASA performs only phase two when either a nondegeneracy assumption holds, or the active constraints are linearly independent and a strong second-order sufficient optimality condition holds.