Title :
On dynamic gradient systems for solving linear programs: a sliding mode analysis
Author :
Chong, Edwin K P ; Hui, Stefen ; Zak, Stanislaw H.
Author_Institution :
Sch. of Electr. Eng. & Comput. Eng., Purdue Univ., West Lafayette, IN, USA
Abstract :
We use sliding modes to analyze a novel class of dynamic gradient systems that solve linear programming problems. The dynamic gradient systems we consider are constructed using a parametric family of exact penalty functions. We prove that for sufficiently large penalty parameters, any trajectory of the dynamic gradient systems associated with a given linear programming problem converges in finite time to its solution set. For our analysis we develop Lyapunov type theorems for finite time convergence of nonsmooth dynamic systems to invariant sets
Keywords :
Lyapunov methods; convergence; linear programming; variable structure systems; Lyapunov type theorems; dynamic gradient systems; dynamic gradient systems trajectory; exact penalty functions parametric family; finite time convergence; invariant sets; linear programming; linear programs; nonsmooth dynamic systems; penalty parameters; sliding mode analysis; Convergence; Differential equations; Dynamic programming; Failure analysis; Linear programming; Sliding mode control;
Conference_Titel :
Decision and Control, 1995., Proceedings of the 34th IEEE Conference on
Conference_Location :
New Orleans, LA
Print_ISBN :
0-7803-2685-7
DOI :
10.1109/CDC.1995.480512
