A hybrid variable penalty method for nonlinear programming

✍ Scribed by B. Prasad

• Publisher: Elsevier Science
• Year: 1982
• Tongue: English
• Weight: 835 KB
• Volume: 8
• Category: Article
• ISSN: 0898-1221
• DOI: 10.1016/0898-1221(82)90017-7

✦ Synopsis

The paper describes a hybrid variable penalty method (in which the penalty functions are finite on the boundary of the constrained set) for solving a general nonlinear programming problem. The method combines two types of variable penalty functions to obtain a hybrid formulation in such a way that the error in the approximation of the Hessian matrix resulting from using only the first derivatives of the constraints. are minimized both in the feasible and infeasible domains. The hybrid algorithm poses a sequence of unconstrained optimization problems with mechanism to control the quality of the approximation for the Hessian matrix. The unconstrained problems are solved using a modified Newton's algorithm. The hybrid method is found to exhibit the following characteristics: (i) Admit small values of the penalty weight r to start SUMT (i.e. r= 1 x 10-j or smaller) with no apparent ill-conditioning; (ii) Stimulate faster rate of convergence for a.single r: (iii) Permit feasible or infeasible initial starting points. The numerical effectiveness of the algorithm is demonstrated on a relatively large set of test problems.