On the Convergence of the Pshenichnyi-Pironneau-Polak Minimax Algorithm with an Active Set Strategy

• Published in: Journal of optimization theory and applications Vol. 138; no. 2; pp. 305 - 309
• Main Author: Polak, E.
• Format: Journal Article
• Language: English
• Published: Boston Springer US 01.08.2008; Springer; Springer Nature B.V
• Subjects: Algorithms; Applications of Mathematics; Applied sciences; Approximation; Calculus of Variations and Optimal Control; Optimization; Computation; Convergence; Engineering; Exact sciences and technology; Mathematical programming; Mathematics; Mathematics and Statistics; Minimax technique; Nonlinear programming; Operational research and scientific management; Operational research. Management science; Operations Research/Decision Theory; Optimization; Optimization algorithms; Proving; Strategy; Studies; Technical Note; Theory of Computation; Active set strategies; Minimax algorithms; Convergence theorems; Minimax problem; Feasible direction method; Minimax method; Minimax strategy; Minimax algorithms .Active set strategies .Convergence theorems; Approximation algorithm; Ellipsoid; Optimization; Convergence; Mathematical programming
• ISSN: 0022-3239; 1573-2878
• DOI: 10.1007/s10957-008-9354-x

The purpose of this technical note is to present a proof of convergence of the Pshenichnyi-Pironneau-Polak (PPP) minimax algorithm (see Algorithm 2.4.1 in Polak, Optimization: Algorithms and Consistent Approximations, Springer, [ 1997 ]), modified to use an active set strategy. This active set strategy was formally derived in Polak (Optimization: Algorithms and Consistent Approximations, Springer, [ 1997 ]) from those used in the methods of feasible directions developed by Zoutendijk (Methods of Feasible Directions, Elsevier, [ 1960 ]) and Polak (Computational Methods in Optimization: A Unified Approach, Academic, [ 1971 ]). The resulting ε -Active PPP algorithm was presented as Algorithm 2.4.34, in Polak (Optimization: Algorithms and Consistent Approximations, Springer, [ 1997 ]), without any proofs.