Direct Numerical Algorithm for Constrained Variational Problems. (3rd April 2017)

• Record Type: Journal Article
• Authors: Pedregal, Pablo
• Is Part Of: Numerical functional analysis and optimization. Volume 38:Number 4(2017)
• Page Start: 486
• Page End: 506
• Publication Date: 2017-04-03
• Subjects: Constrained variational principle -- discretized optimization problem -- exponential barrier -- iterative procedure; 49M30; Functional analysis -- Periodicals; Numerical analysis -- Periodicals; Mathematical optimization -- Periodicals; Numerical Analysis, Computer-Assisted; 515.705
• DOI: 10.1080/01630563.2017.1281824
• Languages: English
• ISSNs: 0163-0563

Abstract

ABSTRACT: We propose a direct treatment for the numerical simulation of optimal solutions for vector, one-dimensional variational problems under pointwise constraints in the form of several inequalities. It is an iterative procedure to approximate the optimal solutions of such variational problems that rely on our ability to efficiently approximate the optimal solutions of variational problems without restrictions, except possibly for end point constraints. One main advantage is that there is no need to control the free boundary, or the contact set, during the iterative process where constraints are active. In addition to proving some convergence results, the scheme is illustrated through several typical situations.