scholarly journals A Branch and Bound Reduced Algorithm for Quadratic Programming Problems with Quadratic Constraints

2013 ◽  
Vol 2013 ◽  
pp. 1-6 ◽  
Author(s):  
Yuelin Gao ◽  
Feifei Li ◽  
Siqiao Jin
Keyword(s):  
Lower Bound ◽  
Quadratic Programming ◽  
Branch And Bound ◽  
Numerical Experiments ◽  
Original Problem ◽  
Degree Of Approximation ◽  
Quadratic Constraints ◽  
Reduction Strategy ◽  
Optimal Value ◽  
Quadratic Programming Problems

We propose a branch and bound reduced algorithm for quadratic programming problems with quadratic constraints. In this algorithm, we determine the lower bound of the optimal value of original problem by constructing a linear relaxation programming problem. At the same time, in order to improve the degree of approximation and the convergence rate of acceleration, a rectangular reduction strategy is used in the algorithm. Numerical experiments show that the proposed algorithm is feasible and effective and can solve small- and medium-sized problems.

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 Optimal control of a chemical reactor

1997 ◽  
Vol 39 (1) ◽  
pp. 61-76
Author(s):  
K. H. Wong ◽  
N. Lock
Keyword(s):  
Optimal Control ◽  
Finite Element ◽  
Differential Equations ◽  
Quadratic Programming ◽  
Original Problem ◽  
Chemical Reactor ◽  
Galerkin Scheme ◽  
Actual Output ◽  
Quadratic Programming Problems ◽  
Linearly Constrained

AbstractA chemical reactor problem is considered governed by partial differential equations. We wish to control the input temperature and the input oxygen concentration so that the actual output temperature can be as close to the desired output temperature as possible. By linearizing the differential equations around a nominal equation and then applying a finite-element Galerkin Scheme to the resulting system, the original problem can be converted into a sequence of linearly-constrained quadratic programming problems.

A Feasible Algorithm for a Class of Mathematical Problems in Mechanical System

2010 ◽  
Vol 26-28 ◽  
pp. 1032-1035
Author(s):  
Jing Ben Yin ◽  
Kun Li ◽  
Hong Wei Jiao ◽  
Yong Qiang Chen
Keyword(s):  
Mechanical System ◽  
Branch And Bound ◽  
Numerical Experiments ◽  
Original Problem ◽  
Mathematical Problem ◽  
Linear Relaxation ◽  
Equivalent Problem ◽  
Mathematical Problems ◽  
Feasible Algorithm ◽  
Bound Theory

In this paper, we proposed an algorithm to globally solve a class of mathematical problems in mechanical system. Firstly, by utilizing equivalent problem and linear relaxation technique, a linear relaxation programming of original mathematical problem is established. Secondly, by using branch and bound theory, a feasible algorithm is proposed for globally solving original problem. Finally, the convergence of the proposed algorithm is proven, and numerical experiments showed that the presented algorithm is feasible.

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