scholarly journals PEMECAHAN MASALAH NONLINEAR PROGRAMMING DENGAN LAGRANGEAN METHOD MENGGUNAKAN SUBSTITUTION METHOD ATAU MICROSOFT EXCEL

2017 ◽  
Vol 4 (2) ◽  
Author(s):  
Rudy Santosa Sudirga
Keyword(s):  
Nonlinear Programming ◽  
Programming Problem ◽  
Lagrange Multipliers ◽  
Optimization Problems ◽  
Stationary Points ◽  
Mathematical Tool ◽  
Nonlinear Programming Problem ◽  
Microsoft Excel ◽  
Substitution Method ◽  
General Technique

<p><em>Lagrange Multipliers are a mathematical tool for constrained optimization of differentiable functions. The given procedure defines the Lagrangean Method for identifying the stationary points of optimization problems with equality constraints; L (ℷ, X) = f(X) – ℷg(X – C). This function is called the Lagrangean function and the parameters ℷ is the Lagrange Multipliers. The partial derivatives of this equation ∂L/∂ℷ = 0 and ∂L/∂X = 0 will give the optimal result for X.</em></p><p><em>However, in some cases, sometimes we have been facing some difficulties to solve nonlinear programming problem with this method, therefore we would like to introduce the <strong>Substitution Method</strong> or <strong>Microsoft Excel Method</strong>, which is simple, easier and faster to solve the nonlinear programming problem. Because of the mathematical nature of nonlinear programming models, and in management science we do not have a single general technique to solve all mathematical models that can arise in practice, therefore simpler approaches should be explored first. In some cases, a “common sense” solution may be reached through simple observations.  </em><em>  </em></p>

scholarly journals Best Proximity Point Results for MK-Proximal Contractions

2012 ◽  
Vol 2012 ◽  
pp. 1-14 ◽  
Author(s):  
Mohamed Jleli ◽  
Erdal Karapınar ◽  
Bessem Samet
Keyword(s):  
Nonlinear Programming ◽  
Programming Problem ◽  
Iterative Algorithm ◽  
Distance Function ◽  
Metric Space ◽  
Optimization Problems ◽  
Best Proximity Point ◽  
Nonlinear Programming Problem ◽  
New Class ◽  
Contractive Mappings

LetAandBbe nonempty subsets of a metric space with the distance function d, andT:A→Bis a given non-self-mapping. The purpose of this paper is to solve the nonlinear programming problem that consists in minimizing the real-valued functionx↦d(x,Tx), whereTbelongs to a new class of contractive mappings. We provide also an iterative algorithm to find a solution of such optimization problems.

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.

scholarly journals Evolutionary Algorithms for Constrained Parameter Optimization Problems

1996 ◽  
Vol 4 (1) ◽  
pp. 1-32 ◽  
Author(s):  
Zbigniew Michalewicz ◽  
Marc Schoenauer
Keyword(s):  
Nonlinear Programming ◽  
Evolutionary Algorithms ◽  
Evolutionary Computation ◽  
Numerical Optimization ◽  
Optimization Problems ◽  
Optimization Techniques ◽  
Test Cases ◽  
Nonlinear Constraints ◽  
Nonlinear Programming Problem ◽  
General Nonlinear Programming

Evolutionary computation techniques have received a great deal of attention regarding their potential as optimization techniques for complex numerical functions. However, they have not produced a significant breakthrough in the area of nonlinear programming due to the fact that they have not addressed the issue of constraints in a systematic way. Only recently have several methods been proposed for handling nonlinear constraints by evolutionary algorithms for numerical optimization problems; however, these methods have several drawbacks, and the experimental results on many test cases have been disappointing. In this paper we (1) discuss difficulties connected with solving the general nonlinear programming problem; (2) survey several approaches that have emerged in the evolutionary computation community; and (3) provide a set of 11 interesting test cases that may serve as a handy reference for future methods.

Minimax Input Shaper Design Using Linear Programming

2008 ◽  
Vol 130 (5) ◽  
Author(s):  
Tarunraj Singh
Keyword(s):  
Linear Programming ◽  
Nonlinear Programming ◽  
Programming Problem ◽  
Linear Programming Problem ◽  
Barycentric Coordinates ◽  
Nonlinear Programming Problem ◽  
Dome A ◽  
Input Shaper ◽  
Maximum Value ◽  
The Cost

The focus of this paper is on the design of robust input shapers where the maximum value of the cost function over the domain of uncertainty is minimized. This nonlinear programming problem is reformulated as a linear programming problem by approximating a n-dimensional hypersphere with multiple hyperplanes (as in a geodesic dome). A recursive technique to approximate a hypersphere to any level of accuracy is developed using barycentric coordinates. The proposed technique is illustrated on the spring-mass-dashpot and the benchmark floating oscillator problem undergoing a rest-to-rest maneuver. It is shown that the results of the linear programming problem are nearly identical to that of the nonlinear programming problem.

Sign in / Sign up

Export Citation Format

Share Document