scholarly journals Saddle Point Optimality Criteria of Interval Valued Non-Linear Programming Problem

2021 ◽  
Vol 38 (3) ◽  
pp. 351-364
Author(s):  
Md Sadikur Rahman ◽  
Emad E. Mahmoud ◽  
Ali Akbar Shaikh ◽  
Abdel-Haleem Abdel-Aty ◽  
Asoke Kumar Bhunia
Keyword(s):  
Linear Programming ◽  
Saddle Point ◽  
Programming Problem ◽  
Linear Programming Problem ◽  
Optimality Criteria ◽  
Non Linear Programming ◽  
Non Linear ◽  
Interval Valued

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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