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 Best Proximity Points for Some Classes of Proximal Contractions

2013 ◽  
Vol 2013 ◽  
pp. 1-10 ◽  
Author(s):  
Maryam A. Alghamdi ◽  
Naseer Shahzad ◽  
Francesca Vetro
Keyword(s):  
Approximate Solution ◽  
Nonlinear Programming ◽  
Programming Problem ◽  
Iterative Algorithm ◽  
Best Proximity Point ◽  
Sufficient Conditions ◽  
Nonlinear Programming Problem ◽  
Optimal Approximate Solution ◽  
Unique Point ◽  
Banach’S Contraction Principle

Given a self-mapping and a non-self-mapping , the aim of this work is to provide sufficient conditions for the existence of a unique point , calledg-best proximity point, which satisfies . In so doing, we provide a useful answer for the resolution of the nonlinear programming problem of globally minimizing the real valued function , thereby getting an optimal approximate solution to the equation . An iterative algorithm is also presented to compute a solution of such problems. Our results generalize a result due to Rhoades (2001) and hence such results provide an extension of Banach's contraction principle to the case of non-self-mappings.

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 Geodesic $ \mathcal{E} $-prequasi-invex function and its applications to non-linear programming problems

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Akhlad Iqbal ◽  
Praveen Kumar
Keyword(s):  
Nonlinear Programming ◽  
Programming Problem ◽  
Sufficient Optimality Condition ◽  
Nonlinear Programming Problem ◽  
Non Linear Programming ◽  
Invex Functions ◽  
New Class ◽  
Invex Set ◽  
Linear Programming Problems ◽  
Invex Function

<p style='text-indent:20px;'>In this article, we define a new class of functions on Riemannian manifolds, called geodesic <inline-formula><tex-math id="M2">\begin{document}$ \mathcal{E} $\end{document}</tex-math></inline-formula>-prequasi-invex functions. By a suitable example it has been shown that it is more generalized class of convex functions. Some of its characteristics are studied on a nonlinear programming problem. We also define a new class of sets, named geodesic slack invex set. Furthermore, a sufficient optimality condition is obtained for a nonlinear programming problem defined on a geodesic local <inline-formula><tex-math id="M3">\begin{document}$ \mathcal{E} $\end{document}</tex-math></inline-formula>-invex set.</p>

Obstacle Avoidance and Minimum Time Control of Cranes Using Flat Outputs and Nonlinear Programming

2004 ◽  
Author(s):  
Randhir Kumar ◽  
K. Kurien Issac
Keyword(s):  
Nonlinear Programming ◽  
Control Problem ◽  
Programming Problem ◽  
Obstacle Avoidance ◽  
Iterative Algorithm ◽  
Minimum Time ◽  
Nonlinear Programming Problem ◽  
Time Control

The problem addressed here is to determine controls for moving a load along specified trajectories which avoid obstacles. It is possible to use flat outputs to determine inputs when hoist motion is present. However, when hoist is locked, the system does not appear to be differentially flat, and hence the above approach could not be used. We propose an iterative algorithm for the problem of calculating trolley motions in this case. Results for load motions requiring (a) travel and traverse of the trolley and hoist, (b) travel and hoist, and (c) travel alone, are presented. We also use flat outputs to formulate the minimum time control problem as a nonlinear programming problem, with constraints arising from limits on trolley and hoist accelerations and velocities, and positive rope tension. Solutions obtained are also presented.

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 Best Proximity Point for Generalized Proximal Weak Contractions in Complete Metric Space

2014 ◽  
Vol 2014 ◽  
pp. 1-6 ◽  
Author(s):  
Erdal Karapınar ◽  
V. Pragadeeswarar ◽  
M. Marudai
Keyword(s):  
Approximate Solution ◽  
Metric Space ◽  
Existence And Uniqueness ◽  
Metric Spaces ◽  
Best Proximity Point ◽  
Complete Metric Space ◽  
Optimal Approximate Solution ◽  
Weak Contraction ◽  
Complete Metric Spaces ◽  
New Class

We introduce a new class of nonself-mappings, generalized proximal weak contraction mappings, and prove the existence and uniqueness of best proximity point for such mappings in the context of complete metric spaces. Moreover, we state an algorithm to determine such an optimal approximate solution designed as a best proximity point. We establish also an example to illustrate our main results. Our result provides an extension of the related results in the literature.

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