scholarly journals A Rank-Two Feasible Direction Algorithm for the Binary Quadratic Programming

2013 ◽  
Vol 2013 ◽  
pp. 1-7
Author(s):  
Xuewen Mu ◽  
Yaling Zhang
Keyword(s):  
Quadratic Programming ◽  
Semidefinite Programming ◽  
Randomized Algorithm ◽  
Feasible Direction ◽  
Semidefinite Programming Relaxation ◽  
Quadratic Constraints ◽  
Binary Quadratic Programming ◽  
Feasible Direction Algorithm ◽  
Max Cut Problem ◽  
Matrix Variable

Based on the semidefinite programming relaxation of the binary quadratic programming, a rank-two feasible direction algorithm is presented. The proposed algorithm restricts the rank of matrix variable to be two in the semidefinite programming relaxation and yields a quadratic objective function with simple quadratic constraints. A feasible direction algorithm is used to solve the nonlinear programming. The convergent analysis and time complexity of the method is given. Coupled with randomized algorithm, a suboptimal solution is obtained for the binary quadratic programming. At last, we report some numerical examples to compare our algorithm with randomized algorithm based on the interior point method and the feasible direction algorithm on max-cut problem. Simulation results have shown that our method is faster than the other two methods.

A feasible direction algorithm for general nonlinear semidefinite programming

2016 ◽  
Vol 55 (4) ◽  
pp. 1261-1279 ◽  
Author(s):  
Jean Rodolphe Roche ◽  
José Herskovits ◽  
Elmer Bazán ◽  
Andrés Zúñiga
Keyword(s):  
Semidefinite Programming ◽  
Feasible Direction ◽  
Nonlinear Semidefinite Programming ◽  
Feasible Direction Algorithm

A General Method for Computing the Distance Between Two Moving Objects Using Optimization Techniques

1992 ◽  
Author(s):  
Ou Ma ◽  
Meyer Nahon
Keyword(s):  
Quadratic Programming ◽  
Moving Objects ◽  
Optimization Techniques ◽  
Quadratic Constraints ◽  
Space Manipulators ◽  
Programming Techniques ◽  
Distance Problem ◽  
A Minor ◽  
Bounding Surfaces ◽  
General Method

Abstract Presented in this paper is a general method used to find the distance between two moving objects. This distance is defined as the length of the shortest path from one object to the other. The objects are assumed to be composed of arbitrary quadratic surface segments. The distance problem is formulated as a quadratic programming problem with linear and/or quadratic constraints, which is solved by efficient and robust quadratic programming techniques. Attention is focused on implementation in order to achieve computational efficiency for real-time applications. Computing tests show that the computational speed of this method is of linear order in terms of the total number of bounding surfaces of the two objects. It is also shown that, with a minor modification, this method can be used to calculate the interference between objects. A corresponding general software code has been implemented, and will be used for kinematics and dynamics modelling and simulation of space manipulators including situations with transient topologies, contact of environment, and capture/release of payloads.

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