NLPQL: A fortran subroutine solving constrained nonlinear programming problems

1986 ◽  
Vol 5 (1-4) ◽  
pp. 485-500 ◽  
Author(s):  
K. Schittkowski
Keyword(s):  
Nonlinear Programming ◽  
Fortran Subroutine ◽  
Constrained Nonlinear Programming

scholarly journals Trust-Region Based Penalty Barrier Algorithm for Constrained Nonlinear Programming Problems: An Application of Design of Minimum Cost Canal Sections

Mathematics ◽  
2021 ◽  
Vol 9 (13) ◽  
pp. 1551
Author(s):  
Bothina El-Sobky ◽  
Yousria Abo-Elnaga ◽  
Abd Allah A. Mousa ◽  
Mohamed A. El-Shorbagy
Keyword(s):  
Nonlinear Programming ◽  
Global Convergence ◽  
Programming Problem ◽  
Trust Region ◽  
Convergence Theory ◽  
Benchmark Problems ◽  
Nonlinear Programming Problem ◽  
Barrier Method ◽  
Starting Point ◽  
Constrained Nonlinear Programming

In this paper, a penalty method is used together with a barrier method to transform a constrained nonlinear programming problem into an unconstrained nonlinear programming problem. In the proposed approach, Newton’s method is applied to the barrier Karush–Kuhn–Tucker conditions. To ensure global convergence from any starting point, a trust-region globalization strategy is used. A global convergence theory of the penalty–barrier trust-region (PBTR) algorithm is studied under four standard assumptions. The PBTR has new features; it is simpler, has rapid convergerce, and is easy to implement. Numerical simulation was performed on some benchmark problems. The proposed algorithm was implemented to find the optimal design of a canal section for minimum water loss for a triangle cross-section application. The results are promising when compared with well-known algorithms.

A Unified Outline of Nonlinear Programming Algorithms

1985 ◽  
Vol 107 (4) ◽  
pp. 449-453 ◽  
Author(s):  
K. Schittkowski
Keyword(s):  
Nonlinear Programming ◽  
Sequential Quadratic Programming ◽  
Gradient Methods ◽  
Reduced Gradient ◽  
Numerical Performance ◽  
Constrained Nonlinear Programming ◽  
Generalized Reduced Gradient ◽  
Performance Results ◽  
Programming Algorithms ◽  
Reduced Gradient Methods

The four most successful approaches for solving the constrained nonlinear programming problem are the penalty, multiplier, sequential quadratic programming, and generalized reduced gradient methods. A general algorithmic frame will be presented, which realizes any of these methods only by specifying a search direction for the variables, a multiplier estimate, and some penalty parameters in each iteration. This approach allows one to illustrate common mathematical features and, on the other hand, serves to explain the different numerical performance results we observe in practice.

Verifiable outsourcing of constrained nonlinear programming by particle swarm optimization in cloud

2017 ◽  
Vol 22 (10) ◽  
pp. 3343-3355 ◽  
Author(s):  
Tao Xiang ◽  
Weimin Zhang ◽  
Shigang Zhong ◽  
Jiyun Yang
Keyword(s):  
Particle Swarm Optimization ◽  
Nonlinear Programming ◽  
Particle Swarm ◽  
Swarm Optimization ◽  
Constrained Nonlinear Programming
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