scholarly journals A parametric linearizing approach for quadratically inequality constrained quadratic programs

2018 ◽  
Vol 16 (1) ◽  
pp. 407-419 ◽  
Author(s):  
Hongwei Jiao ◽  
Rongjiang Chen
Keyword(s):  
Computational Efficiency ◽  
Numerical Results ◽  
Initial Problem ◽  
Linear Programs ◽  
Quadratic Programs ◽  
Relaxation Problem ◽  
Computational Speed ◽  
Global Optima

AbstractIn this paper we propose a new parametric linearizing approach for globally solving quadratically inequality constrained quadratic programs. By utilizing this approach, we can derive the parametric linear programs relaxation problem of the investigated problem. To accelerate the computational speed of the proposed algorithm, an interval deleting rule is used to reduce the investigated box. The proposed algorithm is convergent to the global optima of the initial problem by subsequently partitioning the initial box and solving a sequence of parametric linear programs relaxation problems. Finally, compared with some existing algorithms, numerical results show higher computational efficiency of the proposed algorithm.

scholarly journals Branch-delete-bound algorithm for globally solving quadratically constrained quadratic programs

2017 ◽  
Vol 15 (1) ◽  
pp. 1212-1224 ◽  
Author(s):  
Zhisong Hou ◽  
Hongwei Jiao ◽  
Lei Cai ◽  
Chunyang Bai
Keyword(s):  
Branch And Bound ◽  
Computational Efficiency ◽  
Global Minimum ◽  
Quadratic Function ◽  
Numerical Results ◽  
Linear Programs ◽  
Quadratic Programs ◽  
New Variables ◽  
Quadratically Constrained ◽  
Methods Numerical

Abstract This paper presents a branch-delete-bound algorithm for effectively solving the global minimum of quadratically constrained quadratic programs problem, which may be nonconvex. By utilizing the characteristics of quadratic function, we construct a new linearizing method, so that the quadratically constrained quadratic programs problem can be converted into a linear relaxed programs problem. Moreover, the established linear relaxed programs problem is embedded within a branch-and-bound framework without introducing any new variables and constrained functions, which can be easily solved by any effective linear programs algorithms. By subsequently solving a series of linear relaxed programs problems, the proposed algorithm can converge the global minimum of the initial quadratically constrained quadratic programs problem. Compared with the known methods, numerical results demonstrate that the proposed method has higher computational efficiency.

scholarly journals A Novel Optimization Method for Nonconvex Quadratically Constrained Quadratic Programs

2014 ◽  
Vol 2014 ◽  
pp. 1-11 ◽  
Author(s):  
Hongwei Jiao ◽  
Yong-Qiang Chen ◽  
Wei-Xin Cheng
Keyword(s):  
Branch And Bound ◽  
Computational Efficiency ◽  
Numerical Experiments ◽  
Optimization Method ◽  
Global Optimum ◽  
Branch And Bound Algorithm ◽  
Linear Programs ◽  
Quadratic Programs ◽  
Optimum Point ◽  
Quadratically Constrained

This paper presents a novel optimization method for effectively solving nonconvex quadratically constrained quadratic programs (NQCQP) problem. By applying a novel parametric linearizing approach, the initial NQCQP problem and its subproblems can be transformed into a sequence of parametric linear programs relaxation problems. To enhance the computational efficiency of the presented algorithm, a cutting down approach is combined in the branch and bound algorithm. By computing a series of parametric linear programs problems, the presented algorithm converges to the global optimum point of the NQCQP problem. At last, numerical experiments demonstrate the performance and computational superiority of the presented algorithm.

Thruster and FPSO Hull Interaction

2014 ◽  
Author(s):  
Ye Tian ◽  
Spyros A. Kinnas
Keyword(s):  
Experimental Data ◽  
Hybrid Method ◽  
Computational Efficiency ◽  
Vortex Lattice ◽  
Numerical Results ◽  
Navier Stokes ◽  
Dynamic Positioning ◽  
Lattice Method ◽  
Vortex Lattice Method ◽  
Number Of Cells

A hybrid method which couples a Vortex-Lattice Method (VLM) solver and a Reynolds-Averaged Navier-Stokes (RANS) solver is applied to simulate the interaction between a Dynamic Positioning (DP) thruster and an FPSO hull. The hybrid method could significantly reduce the number of cells to fifth of that in a full blown RANS simulation and thus greatly enhance the computational efficiency. The numerical results are first validated with available experimental data, and then used to assess the significance of the thruster/hull interaction in DP systems.

Application of Hybrid Subgroup Decomposition Method to Gas Cooled Thermal Reactor Problem

2014 ◽  
Author(s):  
Saam Yasseri ◽  
Farzad Rahnema
Keyword(s):  
Transport Equation ◽  
Computational Efficiency ◽  
Decomposition Method ◽  
High Accuracy ◽  
Numerical Results ◽  
New Method ◽  
Thermal Reactor ◽  
Problem Characteristic ◽  
Group Transport ◽  
Subgroup Decomposition

In this paper, a newly developed hybrid subgroup decomposition method is tested in a 1D problem characteristic of gas cooled thermal reactors (GCR). The new method couples an efficient coarse-group eigenvalue calculation with a set of fine-group transport source iterations to unfold the fine-group flux. It is shown that the new method reproduces the fine-group transport solution by iteratively solving the coarse-group quasi transport equation. The numerical results demonstrate that the new method applied to 1D GCR problem is capable of achieving high accuracy while gaining computational efficiency up to 5 times compared to direct fine-group transport calculations.

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.

Checking Geometric Constraints in Layout Design Using Primitives

1996 ◽  
Author(s):  
H. Yim ◽  
A. C. Butler
Keyword(s):  
Computational Efficiency ◽  
Layout Design ◽  
Geometric Constraints ◽  
Parallel Computer ◽  
Test Problems ◽  
Constraint Checking ◽  
Level Of Abstraction ◽  
Computational Speed ◽  
Geometric Primitives ◽  
New Algorithms

Abstract The use of geometric primitives provides representation of objects in layout design at an appropriate level of abstraction, and it allows the use of two new algorithms which permit improvements in computational speed for constraint checking. These algorithms detect intersections between two rectangles and between a rectangle and circle with improved computational efficiency. The use of this pair of algorithms is demonstrated on test problems executed on a parallel computer, and conclusions are drawn regarding the use of geometric primitives for constraint checking in layout design.

Solving the Equivalent Function of Failure Mode Based on Multiple Correlation

2011 ◽  
Vol 488-489 ◽  
pp. 702-705
Author(s):  
Wei Dong Chen ◽  
Jian Cao Li ◽  
Yan Chun Yu
Keyword(s):  
Reliability Analysis ◽  
Failure Mode ◽  
Computational Efficiency ◽  
Numerical Results ◽  
Two Dimensional ◽  
Multiple Correlation ◽  
Equivalent Function ◽  
Correlation Problem ◽  
Dimensional Integral

To solve the problem of equivalent functions of failure mode and low computational efficiency, the coefficient expression of equivalent functions has been derived based on equivalent principle. The concept of multiple correlation was introduced to the reliability analysis of failure mode , the correlation problem between several components and a component has been explained rationally. The display recursive expression of equivalent functions involved two-dimensional integral computation has been given. The high calculation accuracy and efficiency of solving recursive equivalent functions has been indicated according to numerical results.

Thruster and Hull Interaction

2015 ◽  
Vol 137 (4) ◽  
Author(s):  
Ye Tian ◽  
Spyros A. Kinnas
Keyword(s):  
Experimental Data ◽  
Hybrid Method ◽  
Computational Efficiency ◽  
Vortex Lattice ◽  
Numerical Results ◽  
Navier Stokes ◽  
Dynamic Positioning ◽  
Lattice Method ◽  
Vortex Lattice Method ◽  
Number Of Cells

A hybrid method which couples a vortex-lattice method (VLM) solver and a Reynolds-Averaged Navier–Stokes (RANS) solver is applied to simulate the interaction between a dynamic positioning (DP) thruster and a floating production storage and offloading (FPSO) hull. The hybrid method can significantly reduce the number of cells to fifth of that in a full-blown RANS simulation and thus greatly enhance the computational efficiency. The numerical results are first validated with available experimental data, and then used to assess the significance of the thruster/hull interaction in DP systems.

A STUDY ON SENSITIVITY ANALYSIS FOR CONVEX QUADRATIC PROGRAMS

2006 ◽  
Vol 23 (04) ◽  
pp. 439-452
Author(s):  
SUNGMOOK LIM
Keyword(s):  
Sensitivity Analysis ◽  
Interior Point ◽  
The Other ◽  
Linear Programs ◽  
Quadratic Programs ◽  
Input Parameters ◽  
The Relationship

We extend the two similar interior-point approaches to sensitivity analysis originally developed for linear programs to those for convex quadratic programs, where the first approach is the ∊-sensitivity analysis and the other is Yildirim and Todd's. We study the relationship between the bounds on perturbation of the input parameters arising from the extension of Yildirim and Todd's approach and those from the ∊-sensitivity analysis. Furthermore, we prove that Yildirim and Todd's bounds are asymptotically the same as the symmetrized optimal tripartition bounds in the case of a special type of nondegeneracy.

scholarly journals CHC ALGORITHM FOR ANTENNA ARRAY WITH FAILED ELEMENTS OPTIMIZATION

2014 ◽  
pp. 79-85
Author(s):  
Bogdan Artyushenko ◽  
Galina Shilo ◽  
Volodymyr Krischuk
Keyword(s):  
Genetic Algorithm ◽  
Antenna Array ◽  
Computational Efficiency ◽  
Numerical Results ◽  
Working Time

A new CHC based method for optimization of antenna array, with failed elements, is developed. Performances of CHC and canonical genetic algorithm are compared. Numerical results show that CHC gives better results with the same working time. To improve computational efficiency parallelization possibilities are studied.

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