An Interior-Point Method for Nonlinear Constrained Optimization Problem with Trust-Region Mechanism

Journal of Applied & Computational Mathematics

article

Bothina El-Sobky¹  Gehan Ashry¹  Yousria Abo-Elnaga² 

[1] Department of Mathematics, Alexandria University;Department of Basic Science, Higher Technological Institute

关键词: Nonlinear constrained optimization;    Newton method;    Interior-point method;    Trust-Region mechanism;    Coleman-Li matrix;    Global convergence;   

DOI  :  10.37421/2168-9679.22.11.479

来源: Hilaris Publisher

【 摘 要 】

We introduced an algorithm to solve a Non Linear Constrained Optimization (NLCO) problem in this paper. This algorithm follows Das’s idea of Newton’s interiorpointmethod that uses a diagonal matrix of Coleman and Li for NLCO problems. A Trust-Region (T-R) mechanism is used to globalize the algorithm. This algorithmfollows Byrd and Omojokun’s idea of step decomposition. It is a successful idea to overcome the difficulty of having an infeasible quadratic T-R sub problem andconverts the quadratic T-R sub problem into two unconstrained T-R sub problems.A global convergence theory of the algorithm is studied under five standard assumptions. This algorithm is different and maybe simpler than similar ideas such thatthe global convergence theory is not depending on the linear independence assumption on the gradients of the constraints.Some numerical tests are stated to indicate that the algorithm performs effectively and efficiently in pursuance.

【 授权许可】

Unknown