On Projected Newton Barrier Methods for Linear Programming and an Equivalence to Karmarkar's Projective Method.

1985 ◽  
Author(s):  
P. E. Gill ◽  
W. Murray ◽  
M. A. Saunders ◽  
J. A. Tomlin ◽  
M. H. Wright
Keyword(s):  
Linear Programming ◽  
Barrier Methods ◽  
Projective Method

On projected newton barrier methods for linear programming and an equivalence to Karmarkar’s projective method

1986 ◽  
Vol 36 (2) ◽  
pp. 183-209 ◽  
Author(s):  
Philip E. Gill ◽  
Walter Murray ◽  
Michael A. Saunders ◽  
J. A. Tomlin ◽  
Margaret H. Wright
Keyword(s):  
Linear Programming ◽  
Barrier Methods ◽  
Projective Method

Karmarkar's projective method for linear programming: A computational appraisal

1989 ◽  
Vol 16 (1) ◽  
pp. 189-206 ◽  
Author(s):  
Mahesh H. Dodani ◽  
A.J.G. Babu
Keyword(s):  
Linear Programming ◽  
Projective Method

scholarly journals Inverse barrier methods for linear programming

1994 ◽  
Vol 28 (2) ◽  
pp. 135-163 ◽  
Author(s):  
D. Den Hertog ◽  
C. Roos ◽  
T. Terlaky
Keyword(s):  
Linear Programming ◽  
Barrier Methods

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.

Interior methods for constrained optimization

Acta Numerica ◽  
1992 ◽  
Vol 1 ◽  
pp. 341-407 ◽  
Author(s):  
Margaret H. Wright
Keyword(s):  
Linear Programming ◽  
Combinatorial Problems ◽  
Theory And Practice ◽  
Linear Programs ◽  
Great Efficiency ◽  
Barrier Methods ◽  
Interior Method ◽  
Recent Developments ◽  
Interior Methods ◽  
The 1960S

Interior methods for optimization were widely used in the 1960s, primarily in the form of barrier methods. However, they were not seriously applied to linear programming because of the dominance of the simplex method. Barrier methods fell from favour during the 1970s for a variety of reasons, including their apparent inefficiency compared with the best available alternatives. In 1984, Karmarkar's announcement of a fast polynomial-time interior method for linear programming caused tremendous excitement in the field of optimization. A formal connection can be shown between his method and classical barrier methods, which have consequently undergone a renaissance in interest and popularity. Most papers published since 1984 have concentrated on issues of computational complexity in interior methods for linear programming. During the same period, implementations of interior methods have displayed great efficiency in solving many large linear programs of ever-increasing size. Interior methods have also been applied with notable success to nonlinear and combinatorial problems. This paper presents a self-contained survey of major themes in both classical material and recent developments related to the theory and practice of interior methods.

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