A Dual Method for Quadratic Programs with Quadratic Constraints

1975 ◽  
Vol 28 (3) ◽  
pp. 568-576 ◽  
Author(s):  
J. G. Ecker ◽  
R. D. Niemi
Keyword(s):  
Dual Method ◽  
Quadratic Programs ◽  
Quadratic Constraints

scholarly journals An effective algorithm for globally solving quadratic programs using parametric linearization technique

2018 ◽  
Vol 16 (1) ◽  
pp. 1300-1312
Author(s):  
Shuai Tang ◽  
Yuzhen Chen ◽  
Yunrui Guo
Keyword(s):  
Linear Programming ◽  
Optimal Solution ◽  
Route Optimization ◽  
Linear Programming Relaxation ◽  
Effective Algorithm ◽  
Quadratic Programs ◽  
Parametric Linear Programming ◽  
Quadratic Constraints ◽  
Linearization Technique ◽  
Relaxation Problem

AbstractIn this paper, we present an effective algorithm for globally solving quadratic programs with quadratic constraints, which has wide application in engineering design, engineering optimization, route optimization, etc. By utilizing new parametric linearization technique, we can derive the parametric linear programming relaxation problem of the quadratic programs with quadratic constraints. To improve the computational speed of the proposed algorithm, some interval reduction operations are used to compress the investigated interval. By subsequently partitioning the initial box and solving a sequence of parametric linear programming relaxation problems the proposed algorithm is convergent to the global optimal solution of the initial problem. Finally, compared with some known algorithms, numerical experimental results demonstrate that the proposed algorithm has higher computational efficiency.

scholarly journals An Effective Global Optimization Algorithm for Quadratic Programs with Quadratic Constraints

Symmetry ◽  
2019 ◽  
Vol 11 (3) ◽  
pp. 424
Author(s):  
Dongwei Shi ◽  
Jingben Yin ◽  
Chunyang Bai
Keyword(s):  
Numerical Experiments ◽  
Optimal Solution ◽  
Linearization Method ◽  
Linear Programming Relaxation ◽  
Global Optimization Algorithm ◽  
Quadratic Programs ◽  
Global Optimal Solution ◽  
Quadratic Constraints ◽  
Relaxation Problem ◽  
Global Optimal

This paper will present an effective algorithm for globally solving quadratic programs with quadratic constraints. In this algorithm, we propose a new linearization method for establishing the linear programming relaxation problem of quadratic programs with quadratic constraints. The proposed algorithm converges with the global optimal solution of the initial problem, and numerical experiments show the computational efficiency of the proposed algorithm.

On the Heisenberg Supermagnet Model in (2+1)-Dimensions

2017 ◽  
Vol 72 (4) ◽  
pp. 331-337 ◽  
Author(s):  
Zhao-Wen Yan
Keyword(s):  
Integrable System ◽  
Integrable Systems ◽  
Bäcklund Transformations ◽  
Quadratic Constraints ◽  
Backlund Transformations

AbstractThe Heisenberg supermagnet model is an important supersymmetric integrable system in (1+1)-dimensions. We construct two types of the (2+1)-dimensional integrable Heisenberg supermagnet models with the quadratic constraints and investigate the integrability of the systems. In terms of the gage transformation, we derive their gage equivalent counterparts. Furthermore, we also construct new solutions of the supersymmetric integrable systems by means of the Bäcklund transformations.

Sign in / Sign up

Export Citation Format

Share Document