Abstract
The solutions of Linear Programming Problems by the segmentation of the cuboidal response surface through the Super Convergent Line Series methodologies were obtained. The cuboidal response surface was segmented up to four segments, and explored. It was verified that the number of segments, S, for which optimal solutions are obtained is two (S = 2). Illustrative examples and a real-life problem were also given and solved.
Highlights
Linear Programming (LP) problems belong to a class of constrained convex optimization problems which have been widely discussed by several authors: see [1] [2] [3]
The commonly used algorithms for solving Linear Programming problems are: the Simplex method which requires the use of artificial variables and surplus or slack variables, and the active set method which requires the use of artificial constraints and variables
The active set and simplex methods which are available for solving linear programming problems belong to the class of line search exchange algorithms
Summary
Linear Programming (LP) problems belong to a class of constrained convex optimization problems which have been widely discussed by several authors: see [1] [2] [3]. The active set and simplex methods which are available for solving linear programming problems belong to the class of line search exchange algorithms. The line search algorithm, which is built around the concept of super convergence, has several points of departure from the classical, gradient-based line series. [15] proposed a line search algorithm based on the Majorize-Minimum principle; here, a tangent majorant function is built to approximate a scalar criterion containing a barrier function, which leads to a simple line search ensuring the convergence of several classical descent optimization strategies, including the most classical variants of non-linear conjugate gradient. [16] presented the fundamental ideas, concepts and theorems of basic line search algorithm for solving linear programming problems which can be regarded as an extension of the Simplex method. This paper is basically on obtaining optimal solutions and segmentation of Linear Programming Problems in three dimensional spaces of a cuboidal region
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