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Please use this identifier to cite or link to this item: http://hdl.handle.net/123456789/11436

Title: The Role of Concave and Convex Functions in the Study of Linear & Non-Linear Programming
Authors: Owusu-Hemeng, Andrew
Sarpong, Peter Kwasi
Ackora-Prah, Joseph
Issue Date: 5-May-2018
Publisher: Dama International Journal of Researchers (DIJR)
Citation: Dama International Journal of Researchers (DIJR), ISSN: 2343-6743, ISI Impact Factor: 1.018 Vol 3, Issue 05, May, 2018, Pages 15 -29 , Available @ www.damaacademia.com
Abstract: Convex functions appear in many problems in pure and applied mathematics. They play an extremely important role in the study of both linear and non-linear programming problems. It is very important in the study of optimization. The solutions to these problems lie on their vertices. The theory of convex functions is part of the general subject of convexity, since a convex function is one whose epigraph is a convex set. Nonetheless it is an important theory which touches almost all branches of mathematics. Graphical analysis is one of the first topics in mathematics which requires the concept of convexity. Calculus gives us a powerful tool in recognizing convexity, the second-derivative test. Miraculously, this has a natural generalization for the several variables case, the Hessian test. This project is intended to study the basic properties, some definitions, proofs of theorems and some examples of convex functions. Some definitions like convex and concave sets, affine sets, conical sets, concave functions shall be known. It will also prove that the negation of a convex function will generate a concave function and a concave set is a convex set. There is also the preposition that the intersection of convex sets is a convex set but the union of convex sets is not necessarily a convex set. This work is intended to help students acquire more knowledge on convex and concave functions of single variables.
Description: An article published in Dama International Journal of Researchers (DIJR), ISSN: 2343-6743, ISI Impact Factor: 1.018 Vol 3, Issue 05, May, 2018, Pages 15 -29 , Available @ www.damaacademia.com
URI: http://hdl.handle.net/123456789/11436
Appears in Collections:College of Science

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