An Active Set Algorithm for Nonlinear Optimization with Polyhedral Constraints

Abstract

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.

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• The Switch Point Algorithm
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• NPASA: An algorithm for nonlinear programming -- Local Convergence
• NPASA: An algorithm for nonlinear programming -- Motivation and Global Convergence
• A Newton-Type Active Set Method for Nonlinear Optimization with Polyhedral Constraints
• Minimization over the l1-ball using an active-set non-monotone projected gradient