An affine covariant composite step method for optimization with PDEs as equality constraints. (3rd September 2017)

• Record Type: Journal Article
• Authors: Lubkoll, Lars; Schiela, Anton; Weiser, Martin
• Is Part Of: Optimization methods and software. Volume 32:Number 5(2017)
• Page Start: 1132
• Page End: 1161
• Publication Date: 2017-09-03
• Subjects: composite step methods -- cubic regularization -- affine covariant -- optimization with PDEs; 49M37 -- 90C55 -- 90C06; Mathematical optimization -- Periodicals; Algorithms -- Periodicals; 519.7
• DOI: 10.1080/10556788.2016.1241783
• Languages: English
• ISSNs: 1055-6788

Abstract

Abstract : We propose a composite step method, designed for equality constrained optimization with partial differential equations. Focus is laid on the construction of a globalization scheme, which is based on cubic regularization of the objective and an affine covariant damped Newton method for feasibility. We show finite termination of the inner loop and fast local convergence of the algorithm. Numerical results are shown for optimal control problems subject to a nonlinear heat equation.