First, we present the working (active) set method, which reduces the bound-constrained problem to a series of unconstrained problems solved by a direct solver. Then, we introduce the Polyak method, which implements a solution of auxiliary unconstrained problems by conjugate gradients. We show how to speed up the Polyak algorithm by “looking ahead” so it can use inexact solutions to auxiliary problems.

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Active Sets with Finite Termination

  • Zdeněk Dostál

摘要

First, we present the working (active) set method, which reduces the bound-constrained problem to a series of unconstrained problems solved by a direct solver. Then, we introduce the Polyak method, which implements a solution of auxiliary unconstrained problems by conjugate gradients. We show how to speed up the Polyak algorithm by “looking ahead” so it can use inexact solutions to auxiliary problems.