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.

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 A New Global Optimization Algorithm for Solving Generalized Geometric Programming

2010 ◽  
Vol 2010 ◽  
pp. 1-12 ◽  
Author(s):  
San-Yang Liu ◽  
Chun-Feng Wang ◽  
Li-Xia Liu
Keyword(s):  
Global Optimization ◽  
Optimization Algorithm ◽  
Geometric Programming ◽  
Optimal Solution ◽  
Global Optimization Algorithm ◽  
Global Optimal Solution ◽  
Linearization Technique ◽  
Generalized Geometric Programming ◽  
Global Optimal ◽  
Pruning Technique

A global optimization algorithm for solving generalized geometric programming (GGP) problem is developed based on a new linearization technique. Furthermore, in order to improve the convergence speed of this algorithm, a new pruning technique is proposed, which can be used to cut away a large part of the current investigated region in which the global optimal solution does not exist. Convergence of this algorithm is proved, and some experiments are reported to show the feasibility of the proposed algorithm.

scholarly journals Global Minimization for Generalized Polynomial Fractional Program

2014 ◽  
Vol 2014 ◽  
pp. 1-12 ◽  
Author(s):  
Xue-Ping Hou ◽  
Pei-Ping Shen ◽  
Chun-Feng Wang
Keyword(s):  
Optimization Problem ◽  
Optimal Solution ◽  
Efficient Global Optimization ◽  
Global Optimization Algorithm ◽  
Global Optimal Solution ◽  
Program Problem ◽  
Fractional Program ◽  
Generalized Polynomial ◽  
Branch And Bound Search ◽  
Global Optimal

This paper is concerned with an efficient global optimization algorithm for solving a kind of fractional program problem(P), whose objective and constraints functions are all defined as the sum of ratios generalized polynomial functions. The proposed algorithm is a combination of the branch-and-bound search and two reduction operations, based on an equivalent monotonic optimization problem of(P). The proposed reduction operations specially offer a possibility to cut away a large part of the currently investigated region in which the global optimal solution of(P)does not exist, which can be seen as an accelerating device for the solution algorithm of(P). Furthermore, numerical results show that the computational efficiency is improved by using these operations in the number of iterations and the overall execution time of the algorithm, compared with other methods. Additionally, the convergence of the algorithm is presented, and the computational issues that arise in implementing the algorithm are discussed. Preliminary indications are that the algorithm can be expected to provide a practical approach for solving problem(P)provided that the number of variables is not too large.

scholarly journals A New Global Optimization Algorithm for Solving a Class of Nonconvex Programming Problems

2014 ◽  
Vol 2014 ◽  
pp. 1-10
Author(s):  
Xue-Gang Zhou ◽  
Bing-Yuan Cao
Keyword(s):  
Linear Programming ◽  
Nonconvex Programming ◽  
Optimal Solution ◽  
Linearization Method ◽  
Global Optimal Solution ◽  
Natural Logarithm ◽  
Lower Bounding ◽  
Linear Programming Problems ◽  
Global Optimal ◽  
Logarithm Function

A new two-part parametric linearization technique is proposed globally to a class of nonconvex programming problems (NPP). Firstly, a two-part parametric linearization method is adopted to construct the underestimator of objective and constraint functions, by utilizing a transformation and a parametric linear upper bounding function (LUBF) and a linear lower bounding function (LLBF) of a natural logarithm function and an exponential function witheas the base, respectively. Then, a sequence of relaxation lower linear programming problems, which are embedded in a branch-and-bound algorithm, are derived in an initial nonconvex programming problem. The proposed algorithm is converged to global optimal solution by means of a subsequent solution to a series of linear programming problems. Finally, some examples are given to illustrate the feasibility of the presented algorithm.

scholarly journals Quadratic problems with two quadratic constraints: convex quadratic relaxation and strong Lagrangian duality

2020 ◽  
Author(s):  
Abdelouahed Hamdi ◽  
Akram Taati ◽  
Temadher A Almaadeed
Keyword(s):  
Sufficient Conditions ◽  
Optimal Solution ◽  
Lagrangian Duality ◽  
Global Optimality ◽  
Global Optimal Solution ◽  
Quadratic Constraints ◽  
Quadratic Minimization ◽  
Global Optimal ◽  
Necessary And Sufficient ◽  
Convex Quadratic Relaxation

In this paper,  we study  a nonconvex quadratic minimization problem with two quadratic constraints, one of which being convex.  We introduce two convex quadratic relaxations (CQRs) and discuss cases, where the problem is equivalent to exactly one of the CQRs. Particularly, we show that the global optimal  solution can be recovered from an optimal solution of the CQRs. Through this equivalence, we introduce new conditions under which the problem enjoys strong Lagrangian duality, generalizing  the recent  condition  in the literature.  Finally, under the new conditions,  we present  necessary and sufficient conditions for global optimality of the problem.

AO-BBO: A Novel Optimization Algorithm and Its Application in Plant Drug Extraction

2019 ◽  
Vol 19 (2) ◽  
pp. 139-145 ◽  
Author(s):  
Bote Lv ◽  
Juan Chen ◽  
Boyan Liu ◽  
Cuiying Dong
Keyword(s):  
Optimization Algorithm ◽  
Learning Strategy ◽  
Optimal Solution ◽  
Population Diversity ◽  
Global Optimal Solution ◽  
Plant Medicine ◽  
Suitability Index ◽  
Sensing Model ◽  
Local Optimal Solution ◽  
Global Optimal

<P>Introduction: It is well-known that the biogeography-based optimization (BBO) algorithm lacks searching power in some circumstances. </P><P> Material & Methods: In order to address this issue, an adaptive opposition-based biogeography-based optimization algorithm (AO-BBO) is proposed. Based on the BBO algorithm and opposite learning strategy, this algorithm chooses different opposite learning probabilities for each individual according to the habitat suitability index (HSI), so as to avoid elite individuals from returning to local optimal solution. Meanwhile, the proposed method is tested in 9 benchmark functions respectively. </P><P> Result: The results show that the improved AO-BBO algorithm can improve the population diversity better and enhance the search ability of the global optimal solution. The global exploration capability, convergence rate and convergence accuracy have been significantly improved. Eventually, the algorithm is applied to the parameter optimization of soft-sensing model in plant medicine extraction rate. Conclusion: The simulation results show that the model obtained by this method has higher prediction accuracy and generalization ability.</P>

scholarly journals Best Proximity Point Results in Complex Valued Metric Spaces

2014 ◽  
Vol 2014 ◽  
pp. 1-6 ◽  
Author(s):  
Binayak S. Choudhury ◽  
Nikhilesh Metiya ◽  
Pranati Maity
Keyword(s):  
Minimum Distance ◽  
Metric Spaces ◽  
Optimal Solution ◽  
Global Optimal Solution ◽  
Complex Valued Metric Space ◽  
Fixed Point Equation ◽  
Point Equation ◽  
Global Optimal ◽  
Metric Function ◽  
Complex Valued

We introduce the concept of proximity points for nonself-mappings between two subsets of a complex valued metric space which is a recently introduced extension of metric spaces obtained by allowing the metric function to assume values from the field of complex numbers. We apply this concept to obtain the minimum distance between two subsets of the complex valued metric spaces. We treat the problem as that of finding the global optimal solution of a fixed point equation although the exact solution does not in general exist. We also define and use the concept of P-property in such spaces. Our results are illustrated with examples.

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