Open AccessOn the bang-bang control approach via a component-wise line search strategy for unconstrained optimization
Author(s) -
M. S. Lee,
Hendra G. Harno,
B. S. Goh,
King Hann Lim
Publication year - 2021
Publication title -
numerical algebra, control and optimization
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.303
H-Index - 20
eISSN - 2155-3289
pISSN - 2155-3297
DOI - 10.3934/naco.2020014
Subject(s) - optimal control , mathematical optimization , trajectory optimization , convergence (economics) , a priori and a posteriori , mathematics , monotonic function , bang–bang control , optimization problem , function (biology) , control variable , trajectory , line search , control theory (sociology) , computer science , control (management) , path (computing) , mathematical analysis , philosophy , statistics , physics , epistemology , astronomy , evolutionary biology , artificial intelligence , economics , biology , economic growth , programming language
A bang-bang iteration method equipped with a component-wise line search strategy is introduced to solve unconstrained optimization problems. The main idea of this method is to formulate an unconstrained optimization problem as an optimal control problem to obtain an optimal trajectory. However, the optimal trajectory can only be generated by impulsive control variables and it is a straight line joining a guessed initial point to a minimum point. Thus, a priori bounds are imposed on the control variables in order to obtain a feasible solution. As a result, the optimal trajectory is made up of bang-bang control sub-arcs, which form an iterative model based on the Lyapunov function's theorem. This is to ensure monotonic decrease of the objective function value and convergence to a desirable minimum point. However, a chattering behavior may occur near the solution. To avoid this behavior, the Newton iterations are then applied to the proposed method via a two-phase approach to achieve fast convergence. Numerical experiments show that this new approach is efficient and cost-effective to solve the unconstrained optimization problems.