Decomposition Procedure for Solving NLP and QP Problems based on Lagrange and Sander's Method

Decomposition Procedure for Solving NLP and QP Problems based on Lagrange and Sander's Method

H. K. Das (Department of Mathematics, University of Dhaka, Dhaka, Bangladesh)
DOI: 10.4018/IJORIS.2016100103
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Abstract

This paper develops a decompose procedure for finding the optimal solution of convex and concave Quadratic Programming (QP) problems together with general Non-linear Programming (NLP) problems. The paper also develops a sophisticated computer technique corresponding to the author's algorithm using programming language MATHEMATICA. As for auxiliary by making comparison, the author introduces a computer-oriented technique of the traditional Karush-Kuhn-Tucker (KKT) method and Lagrange method for solving NLP problems. He then modify the Sander's algorithm and develop a new computational technique to evaluate the performance of the Sander's algorithm for solving NLP problems. The author observe that the technique avoids some certain numerical difficulties in NLP and QP. He illustrates a number of numerical examples to demonstrate his method and the modified algorithm.
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Literature Review

In 1975, Huang and Aggerwal developed a class of quadratic convergent algorithm for constrained function minimization. Jennergren, L Peter developed a price schedules decomposition algorithm for LP in 1973. In 2013, H. K. Das and M. B. Hasan developed a generalized technique for solving unconstrained NLP problems and again in 2014, H. K. Das, T. Saha and M. B. Hasan worked on 1-D simplex search and its numerical experiments through computer algebra. In 2015, H. K. Das and M. B. Hasan developed an algorithmic technique for solving NLP and QP problems. In 2005, Wang, Chen, Wee and K.-J. Wang proposed a non-linear stochastic optimization algorithm named Stochastic Portfolio Genetic Algorithm (SPGA) to determine a profitable portfolio selection planning plan under risk. In 2012, Gina, Carlos, Barbosa-Correa and Humberto developed a NLP model that addresses to attain the balance between the costs associated with their application and the potential economic losses caused by failing to satisfy customers' quality levels. In 2013, H. K. Das and M. B. Hasan introduced a decomposition approach and its Computer Technique for Solving Primal Dual LP & Linear Fractional Programming (LFP) problems.

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