Approximate and Exact Solution to Non-Linear Programming Problem with Separable Objective Function

1961 ◽  
Vol 43 (1) ◽  
pp. 57 ◽  
Author(s):  
Dan Yaron ◽  
Earl O. Heady
Keyword(s):  
Exact Solution ◽  
Linear Programming ◽  
Objective Function ◽  
Programming Problem ◽  
Linear Programming Problem ◽  
Non Linear Programming ◽  
Non Linear ◽  
Separable Objective Function

scholarly journals TRANSFORMASI LINIER UNTUK PERSOALAN PROGRAM KUADRATIK NOL-SATU

2017 ◽  
Vol 3 (2) ◽  
Author(s):  
M Khahfi Zuhanda
Keyword(s):  
Linear Programming ◽  
Quadratic Programming ◽  
Objective Function ◽  
Programming Problem ◽  
Linear Programming Problem ◽  
Interesting Issue ◽  
Non Linear Programming ◽  
Quadratic Equations ◽  
Non Linear ◽  
Special Case

Program non linier merupakan persoalan yang cukup menarik untuk di bahas oleh matematikawan. Salah satunya program kuadratik nol-satu yang fungsi tujuan dan kendala berbentuk persamaan kuadratik. Program kuadratik nol-satu merupakan kelas khusus dalam pemrograman non-linier karena persyaratan peubah keputusan bernilai nol-satu. Tulisan ini akan mengajukan sebuah teknik untuk menyelesaikan persoalan program kuadratik nol-satu yang dikembangkan oleh Sherali dan Smith. Teknik ini mengubah Quadratic Problems (QP) menjadi kebentuk Bilinier Problems(BP) terlebih dahulu. Akhir dari proses ini mengakibatkan transformasi  program kuadratik nol-satu menjadi persoalan linier nol-satu. Kata Kunci :  integer, linierisasi, nol-satu, program kuadratik  ABSTRACT Non-linear programming is an interesting issue to be discussed by mathematician. One of them is a zero-one quadratic programming, where the objective function and constraints are quadratic equations. The zero-one quadratic programming is a special case in non-linear programming because of the requirement of value variable is zero-one. This paper propose a technique for solving the zero-one quadratic programming problem was developed by Sherali and Smith. This technique converts the Quadratic Problems (QP) into Bilinier Problems (BP) first. The end of this process will transfrom zero-one quadratic programming to zero-one linear programming problem Keywords: Integer, Linearization, Quadratic Programming, Zero-One, 

scholarly journals A comparative study of the methods of solving non-linear programming problem

1970 ◽  
Vol 4 (1) ◽  
pp. 28-34
Author(s):  
Bimal Chandra Das
Keyword(s):  
Linear Programming ◽  
Quadratic Programming ◽  
Comparative Study ◽  
Programming Problem ◽  
Linear Programming Problem ◽  
Feasible Region ◽  
Non Linear Programming ◽  
Condition Method ◽  
Non Linear ◽  
Matlab Programming

The work present in this paper is based on a comparative study of the methods of solving Non-linear programming (NLP) problem. We know that Kuhn-Tucker condition method is an efficient method of solving Non-linear programming problem. By using Kuhn-Tucker conditions the quadratic programming (QP) problem reduced to form of Linear programming(LP) problem, so practically simplex type algorithm can be used to solve the quadratic programming problem (Wolfe's Algorithm).We have arranged the materials of this paper in following way. Fist we discuss about non-linear programming problems. In second step we discuss Kuhn- Tucker condition method of solving NLP problems. Finally we compare the solution obtained by Kuhn- Tucker condition method with other methods. For problem so consider we use MATLAB programming to graph the constraints for obtaining feasible region. Also we plot the objective functions for determining optimum points and compare the solution thus obtained with exact solutions. Keywords: Non-linear programming, objective function ,convex-region, pivotal element, optimal solution. DOI: 10.3329/diujst.v4i1.4352 Daffodil International University Journal of Science and Technology Vol.4(1) 2009 pp.28-34

ON NON-QUADRATIC PENALTY FUNCTION FOR NON-LINEAR PROGRAMMING PROBLEM WITH EQUALITY CONSTRAINTS

2019 ◽  
Vol 7 (1) ◽  
pp. 23-28
Author(s):  
Raju Prajapati ◽  
Om Prakash Dubey ◽  
Ranjit Pradhan
Keyword(s):  
Linear Programming ◽  
Programming Problem ◽  
Linear Programming Problem ◽  
Penalty Method ◽  
Equality Constraints ◽  
Test Problems ◽  
Barrier Methods ◽  
Non Linear Programming ◽  
Non Linear ◽  
Quadratic Penalty Method

Purpose: The present paper focuses on the Non-Linear Programming Problem (NLPP) with equality constraints. NLPP with constraints could be solved by penalty or barrier methods. Methodology: We apply the penalty method to the NLPP with equality constraints only. The non-quadratic penalty method is considered for this purpose. We considered a transcendental i.e. exponential function for imposing the penalty due to the constraint violation. The unconstrained NLPP obtained in this way is then processed for further solution. An improved version of evolutionary and famous meta-heuristic Particle Swarm Optimization (PSO) is used for the same. The method is tested with the help of some test problems and mathematical software SCILAB. The solution is compared with the solution of the quadratic penalty method. Results: The results are also compared with some existing results in the literature.

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