A global optimization approach for solving the convex multiplicative programming problem

1991 ◽  
Vol 1 (4) ◽  
pp. 341-357 ◽  
Author(s):  
Nguyen Van Thoai
Keyword(s):  
Global Optimization ◽  
Programming Problem ◽  
Optimization Approach ◽  
Multiplicative Programming ◽  
Convex Multiplicative Programming

scholarly journals A Global Optimization Approach for Solving Generalized Nonlinear Multiplicative Programming Problem

2014 ◽  
Vol 2014 ◽  
pp. 1-14 ◽  
Author(s):  
Lin-Peng Yang ◽  
Pei-Ping Shen ◽  
Yong-Gang Pei
Keyword(s):  
Global Optimization ◽  
Programming Problem ◽  
Convex Programming ◽  
Optimization Approach ◽  
Linear Programs ◽  
Convex Programming Problem ◽  
Multiplicative Programming ◽  
Main Work ◽  
Reverse Convex Programming ◽  
Reverse Convex

This paper presents a global optimization algorithm for solving globally the generalized nonlinear multiplicative programming (MP) with a nonconvex constraint set. The algorithm uses a branch and bound scheme based on an equivalently reverse convex programming problem. As a result, in the computation procedure the main work is solving a series of linear programs that do not grow in size from iterations to iterations. Further several key strategies are proposed to enhance solution production, and some of them can be used to solve a general reverse convex programming problem. Numerical results show that the computational efficiency is improved obviously by using these strategies.

A Global Optimization Approach for Solving the D.C. Multiplicative Programming Problem

2013 ◽  
Vol 765-767 ◽  
pp. 1196-1199
Author(s):  
Xue Gang Zhou
Keyword(s):  
Global Optimization ◽  
Programming Problem ◽  
Outer Approximation ◽  
Convex Compact ◽  
Feasible Region ◽  
Optimization Approach ◽  
Auxiliary Variables ◽  
Global Optimization Algorithm ◽  
Multiplicative Programming ◽  
Outer Approximation Algorithm

In this paper, we present a global optimization algorithm for solving the D.C. multiplicative programming (DCMP) over a convex compact subset. By introducing auxiliary variables, we give a transformation under which both the objective and the feasible region turn to be d.c.Then we solve equivalent D.C. programming problem by branch and bound method and outer approximation algorithm.

scholarly journals Global Algorithm for Generalized Affine Multiplicative Programming Problem

IEEE Access ◽  
2019 ◽  
Vol 7 ◽  
pp. 162245-162253 ◽  
Author(s):  
Jingben Yin ◽  
Hongwei Jiao ◽  
Youlin Shang
Keyword(s):  
Programming Problem ◽  
Multiplicative Programming ◽  
Global Algorithm

scholarly journals A Global Optimization Algorithm for Sum of Linear Ratios Problem

2013 ◽  
Vol 2013 ◽  
pp. 1-7 ◽  
Author(s):  
Yuelin Gao ◽  
Siqiao Jin
Keyword(s):  
Global Optimization ◽  
Lower Bound ◽  
Programming Problem ◽  
Branch And Bound ◽  
Numerical Experiments ◽  
Original Problem ◽  
Bilinear Programming ◽  
Global Optimization Algorithm ◽  
Product Function ◽  
Optimal Value

We equivalently transform the sum of linear ratios programming problem into bilinear programming problem, then by using the linear characteristics of convex envelope and concave envelope of double variables product function, linear relaxation programming of the bilinear programming problem is given, which can determine the lower bound of the optimal value of original problem. Therefore, a branch and bound algorithm for solving sum of linear ratios programming problem is put forward, and the convergence of the algorithm is proved. Numerical experiments are reported to show the effectiveness of the proposed algorithm.

scholarly journals A Global Optimization Approach to Solve Multi-Aircraft Routing Problems

2010 ◽  
pp. 237-259
Author(s):  
S.P. Wilson ◽  
M.C. Bartholomew-Biggs ◽  
S.C. Parkhurst
Keyword(s):  
Global Optimization ◽  
Real Life ◽  
Two Dimensions ◽  
Numerical Results ◽  
Solution Technique ◽  
Optimization Approach ◽  
Routing Problem ◽  
Aircraft Routing ◽  
Optimization Calculation ◽  
Multiple Routes

This chapter describes the formulation and solution of a multi-aircraft routing problem which is posed as a global optimization calculation. The chapter extends previous work (involving a single aircraft using two dimensions) which established that the algorithm DIRECT is a suitable solution technique. The present work considers a number of ways of dealing with multiple routes using different problem decompositions. A further enhancement is the introduction of altitude to the problems so that full threedimensional routes can be produced. Illustrative numerical results are presented involving up to three aircraft and including examples which feature routes over real-life terrain data.

Sign in / Sign up

Export Citation Format

Share Document