Practical Algorithms : for Sum-of-Ratios and Multiplicative Programming Problems

Yunchol Jong

ISBN 10: 6208847435 / ISBN 13: 9786208847432

Published by Scholars' Press, 2025

About this Item

nach der Bestellung gedruckt Neuware - Printed after ordering - The SoR (Sum-of-Ratios) problem intended to minimize (maximize) a sum of several fractional functions in convex set is a non-convex optimization problem that is difficult to solve by traditional optimization methods. The CMP (Convex Multiplicative Programming) problem is to minimize the sum of products of two convex functions in convex set. The SoR and CMP problems arise in many applications such as the communication, robotics, computer graphics, finance, engineering, plant layout design, robust optimization, VLSI chip design, data mining and so on.This book presents new parametric approach to the SoR and CMP problem. Compared with existing methods based on branch-and-bound procedure and other approaches, the idea of new method is to reduce the SoR and CMP problems to parametric convex programming problem having parameters in objective functions. The parametric algorithm is based on Newton-like method for solving a system of nonlinear equations with parameters and it needs to solve convex programming problem in each iteration. This new algorithm has the global linear and local superlinear/quadratic rate of convergence.

Seller Inventory # 9786208847432

Bibliographic Details

• Title: Practical Algorithms : for Sum-of-Ratios and Multiplicative Programming Problems
• Publisher: Scholars' Press
• Publication Date: 2025
• Language: English
• ISBN 10: 6208847435
• ISBN 13: 9786208847432
• Binding: Taschenbuch
• Condition: Neu
• Dimensions: 220W x 150H x 8D millimeters 220 millimeters width by 150 millimeters height by 8 millimeters depth
• Weight: 209 grams

About this title

Synopsis

The SoR (Sum-of-Ratios) problem intended to minimize (maximize) a sum of several fractional functions in convex set is a non-convex optimization problem that is difficult to solve by traditional optimization methods. The CMP (Convex Multiplicative Programming) problem is to minimize the sum of products of two convex functions in convex set. The SoR and CMP problems arise in many applications such as the communication, robotics, computer graphics, finance, engineering, plant layout design, robust optimization, VLSI chip design, data mining and so on.This book presents new parametric approach to the SoR and CMP problem. Compared with existing methods based on branch-and-bound procedure and other approaches, the idea of new method is to reduce the SoR and CMP problems to parametric convex programming problem having parameters in objective functions. The parametric algorithm is based on Newton-like method for solving a system of nonlinear equations with parameters and it needs to solve convex programming problem in each iteration. This new algorithm has the global linear and local superlinear/quadratic rate of convergence.