Global optimality conditions and optimization methods for polynomial programming problems
- Authors: Wu, Zhiyou , Tian, Jing , Ugon, Julien
- Date: 2015
- Type: Text , Journal article
- Relation: Journal of Global Optimization Vol. 62, no. 4 (2015), p. 617-641
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- Description: This paper is concerned with the general polynomial programming problem with box constraints, including global optimality conditions and optimization methods. First, a necessary global optimality condition for a general polynomial programming problem with box constraints is given. Then we design a local optimization method by using the necessary global optimality condition to obtain some strongly or -strongly local minimizers which substantially improve some KKT points. Finally, a global optimization method, by combining the new local optimization method and an auxiliary function, is designed. Numerical examples show that our methods are efficient and stable.
Global optimality conditions and optimization methods for constrained polynomial programming problems
- Authors: Wu, Zhiyou , Tian, Jing , Ugon, Julien , Zhang, Liang
- Date: 2015
- Type: Text , Journal article
- Relation: Applied Mathematics and Computation Vol. 262, no. (2015), p. 312-325
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- Description: The general constrained polynomial programming problem (GPP) is considered in this paper. Problem (GPP) has a broad range of applications and is proved to be NP-hard. Necessary global optimality conditions for problem (GPP) are established. Then, a new local optimization method for this problem is proposed by exploiting these necessary global optimality conditions. A global optimization method is proposed for this problem by combining this local optimization method together with an auxiliary function. Some numerical examples are also given to illustrate that these approaches are very efficient. (C) 2015 Elsevier Inc. All rights reserved.
Optimality conditions and optimization methods for quartic polynomial optimization
- Authors: Wu, Zhiyou , Tian, Jing , Quan, Jing , Ugon, Julien
- Date: 2014
- Type: Text , Journal article
- Relation: Applied Mathematics and Computation Vol. 232, no. (2014), p. 968-982
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- Description: In this paper multivariate quartic polynomial optimization program (QPOP) is considered. Quartic optimization problems arise in various practical applications and are proved to be NP hard. We discuss necessary global optimality conditions for quartic problem (QPOP). And then we present a new (strongly or ε-strongly) local optimization method according to necessary global optimality conditions, which may escape and improve some KKT points. Finally we design a global optimization method for problem (QPOP) by combining the new (strongly or ε-strongly) local optimization method and an auxiliary function. Numerical examples show that our algorithms are efficient and stable.
An integral function and vector sequence method for unconstrained global optimization
- Authors: Yang, Yongjian , Bai, Fusheng
- Date: 2011
- Type: Text , Journal article
- Relation: Journal of Global Optimization Vol. 50, no. 2 (2011), p. 293-311
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- Description: An integral function and a vector sequence are constructed in this paper. Their theoretical and numerical properties are investigated. Based on the integral function and the vector sequence, an algorithm is proposed for solving a class of unconstrained global optimization problems. For the algorithm, convergence to a global minimizer is discussed under some conditions. Some typical examples are tested to illustrate the efficiency of the algorithm. © Springer Science+Business Media, LLC. 2010.
The effects of the no-touch gap on the no-touch bipolar radiofrequency ablation treatment of liver cancer : a numerical study using a two compartment model
- Authors: Yap, Shelley , Cheong, Jason , Foo, Ji , Ooi, Ean Tat , Ooi, Ean Hin
- Date: 2020
- Type: Text , Journal article
- Relation: Applied Mathematical Modelling Vol. 78, no. (2020), p. 134-147
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- Description: The no-touch bipolar radiofrequency ablation (RFA) for cancer treatment is advantageous primarily because of its capability to prevent tumour track seeding (TTS). In this technique, the RF probes are placed at a distance (no-touch gap) away from the tumour boundary. Ideally, the RF probes should be placed sufficiently far from the tumour in order to avoid TTS. However, having a gap that is too large can lead to ineffective ablation. This paper investigates how the selection of the no-touch gap can affect the tissue electrical and thermal responses during the no-touch bipolar RFA treatment. Simulations were carried out on a two compartment model using the finite element method. Results obtained indicated that a gap that is too large may lead to incomplete ablation and failure to achieve significant ablation margin. However, keeping the gap to be too small may not be clinically practical. It was suggested that the incomplete ablation and the insufficient ablation margin observed in some of the cases may require the placement of additional probes around the tumour. The present study stresses on the importance of identifying the optimal no-touch gap that can avoid TTS without compromising the treatment outcome. © 2019 Elsevier Inc.
A pupil-positioning method based on the starburst model
- Authors: Yu, Pingping , Duan, Wenjie , Sun, Yi , Cao, Ning , Wang, Zhenzhou , Lu, Guojun
- Date: 2020
- Type: Text , Journal article
- Relation: Cmc-Computers Materials & Continua Vol. 64, no. 2 (2020), p. 1199-1217
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- Description: Human eye detection has become an area of interest in the field of computer vision with an extensive range of applications in human-computer interaction, disease diagnosis, and psychological and physiological studies. Gaze-tracking systems are an important research topic in the human-computer interaction field. As one of the core modules of the head-mounted gaze-tracking system, pupil positioning affects the accuracy and stability of the system. By tracking eye movements to better locate the center of the pupil, this paper proposes a method for pupil positioning based on the starburst model. The method uses vertical and horizontal coordinate integral projections in the rectangular region of the human eye for accurate positioning and applies a linear interpolation method that is based on a circular model to the reflections in the human eye. In this paper, we propose a method for detecting the feature points of the pupil edge based on the starburst model, which clusters feature points and uses the RANdom SAmple Consensus (RANSAC) algorithm to perform ellipse fitting of the pupil edge to accurately locate the pupil center. Our experimental results show that the algorithm has higher precision, higher efficiency and more robustness than other algorithms and excellent accuracy even when the image of the pupil is incomplete.
- Description: Science and Technology Support Plan Project of Hebei Province (grant numbers 17210803D and 19273703D Science and Technology Spark Project of the Hebei Seismological Bureau (grant number DZ20180402056) Education Department of Hebei Province (grant number QN2018095) Polytechnic College of Hebei University of Science and Technology
Global optimal solutions to a class of quadrinomial minimization problems with one quadratic constraint
- Authors: Yuan, Y. B. , Fang, Shucherng , Gao, David
- Date: 2012
- Type: Text , Journal article
- Relation: Journal of Global Optimization Vol. 52, no. 2 (2012), p. 195-209
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- Description: This paper studies the canonical duality theory for solving a class of quadri- nomial minimization problems subject to one general quadratic constraint. It is shown that the nonconvex primal problem in Rn can be converted into a concave maximization dual problem over a convex set in R2 , such that the problem can be solved more efficiently. The existence and uniqueness theorems of global minimizers are provided using the triality theory. Examples are given to illustrate the results obtained. © 2011 Springer Science+Business Media, LLC.
A new method for solving linear ill-posed problems
- Authors: Zhang, Jianjun , Mammadov, Musa
- Date: 2012
- Type: Text , Journal article
- Relation: Applied Mathematics and Computation Vol. 218, no. 20 (2012), p.10180-10187
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- Description: In this paper, we propose a new method for solving large-scale ill-posed problems. This method is based on the Karush-Kuhn-Tucker conditions, Fisher-Burmeister function and the discrepancy principle. The main difference from the majority of existing methods for solving ill-posed problems is that, we do not need to choose a regularization parameter in advance. Experimental results show that the proposed method is effective and promising for many practical problems. © 2012.
A BMI approach to guaranteed cost control of discrete-time uncertain system with both state and input delays
- Authors: Zhou, Xiaojun , Dong, Tianxue , Tang, Xiaolin , Yang, Chunhua , Gui, Weihua
- Date: 2015
- Type: Text , Journal article
- Relation: Optimal Control Applications and Methods Vol. 36, no. 6 (2015), p. 844-852
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- Description: In this study, the guaranteed cost control of discrete time uncertain system with both state and input delays is considered. Sufficient conditions for the existence of a memoryless state feedback guaranteed cost control law are given in the bilinear matrix inequality form, which needs much less auxiliary matrix variables and storage space. Furthermore, the design of guaranteed cost controller is reformulated as an optimization problem with a linear objective function, bilinear, and linear matrix inequalities constraints. A nonlinear semi-definite optimization solver - PENLAB is used as a solution technique. A numerical example is given to demonstrate the effectiveness of the proposed method. Copyright © 2014 John Wiley & Sons, Ltd.
Canonical primal-dual algorithm for solving fourth-order polynomial minimization problems
- Authors: Zhou, Xiaojun , Gao, David , Yang, Chunhua
- Date: 2014
- Type: Text , Journal article
- Relation: Applied Mathematics and Computation Vol. 227, no. (2014), p. 246-255
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- Description: This paper focuses on implementation of a general canonical primal-dual algorithm for solving a class of fourth-order polynomial minimization problems. A critical issue in the canonical duality theory has been addressed, i.e., in the case that the canonical dual problem has no interior critical point in its feasible space Sa+, a quadratic perturbation method is introduced to recover the global solution through a primal-dual iterative approach, and a gradient-based method is further used to refine the solution. A series of test problems, including the benchmark polynomials and several instances of the sensor network localization problems, have been used to testify the effectiveness of the proposed algorithm. © 2013 Published by Elsevier Inc. All rights reserved.
Global solutions to a class of CEC benchmark constrained optimization problems
- Authors: Zhou, Xiaojun , Gao, David , Yang, Chunhua
- Date: 2016
- Type: Text , Journal article
- Relation: Optimization Letters Vol. 10, no. 3 (2016), p. 457-472
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- Description: This paper aims to solve a class of CEC benchmark constrained optimization problems that have been widely studied by nature-inspired optimization algorithms. Based on canonical duality theory, these challenging problems can be reformulated as a unified canonical dual problem over a convex set, which can be solved deterministically to obtain global optimal solutions in polynomial time. Applications are illustrated by some well-known CEC benchmark problems, and comparisons with other methods have demonstrated the effectiveness of the proposed approach. © 2014, Springer-Verlag Berlin Heidelberg.
Applying the canonical dual theory in optimal control problems
- Authors: Zhu, Jinghao , Wu, Dan , Gao, David
- Date: 2012
- Type: Text , Journal article
- Relation: Journal of global optimization Vol. 54, no. 2 (2012), p. 221-233
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- Description: This paper presents some applications of the canonical dual theory in optimal control problems. The analytic solutions of several nonlinear and nonconvex problems are investigated by global optimizations. It turns out that the backward differential flow defined by the KKT equation may reach the globally optimal solution. The analytic solution to an optimal control problem is obtained via the expression of the co-state. Some examples are illustrated.
Global optimization over a box via canonical dual function
- Authors: Zhu, Jinghao , Wang, Chao , Gao, David
- Date: 2011
- Type: Text , Journal article
- Relation: Journal of Computational and Applied Mathematics Vol. 235, no. 5 (January 2011), p. 1141-1147
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- Description: In this paper, we study global concave optimization by the canonical dual function. A differential flow on the dual feasible space is introduced. We show that the flow reaches a global minimizer of the concave function over a box. An example is illustrated.
To be fair or efficient or a bit of both
- Authors: Zukerman, Moshe , Mammadov, Musa , Tan, Liansheng , Ouveysi, Iradj , Andrew, Lachlan
- Date: 2008
- Type: Text , Journal article
- Relation: Computers and Operations Research Vol. 35, no. 12 (2008), p. 3787-3806
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- Description: IIntroducing a new concept of (®, ¯)-fairness, which allows for a bounded fairness compromise, so that a source is allocated a rate neither less than 0 · ® · 1, nor more than ¯ ¸ 1, times its fair share, this paper provides a framework to optimize efficiency (utilization, throughput or revenue) subject to fairness constraints in a general telecommunications network for an arbitrary fairness criterion and cost functions. We formulate a non-linear program (NLP) that finds the optimal bandwidth allocation by maximizing efficiency subject to (®, ¯)-fairness constraints. This leads to what we call an efficiency-fairness function, which shows the benefit in efficiency as a function of the extent to which fairness is compromised. To solve the NLP we use two algorithms. The first is a well known branch-and-bound-based algorithm called Lipschitz Global Optimization and the second is a recently developed algorithm called Algorithm for Global Optimization Problems (AGOP). We demonstrate the applicability of the framework to a range of example from sharing a single link to efficiency fairness issues associated with serving customers in remote communities.
- Description: C1
The new robust conic GPLM method with an application to finance : prediction of credit default
- Authors: Özmen, Ay , Weber, Gerhard-Wilhelm , Çavu , Defterli, Özlem
- Date: 2012
- Type: Text , Journal article
- Relation: Journal of Global Optimization Vol.56, no. 2 (2012), p. 233–249
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- Description: This paper contributes to classification and identification in modern finance through advanced optimization. In the last few decades, financial misalignments and, thereby, financial crises have been increasing in numbers due to the rearrangement of the financial world. In this study, as one of the most remarkable of these, countries' debt crises, which result from illiquidity, are tried to predict with some macroeconomic variables. The methodology consists of a combination of two predictive regression models, logistic regression and robust conic multivariate adaptive regression splines (RCMARS), as linear and nonlinear parts of a generalized partial linear model. RCMARS has an advantage of coping with the noise in both input and output data and of obtaining more consistent optimization results than CMARS. An advanced version of conic generalized partial linear model which includes robustification of the data set is introduced: robust conic generalized partial linear model (RCGPLM). This new model is applied on a data set that belongs to 45 emerging markets with 1,019 observations between the years 1980 and 2005. © 2012 Springer Science+Business Media, LLC.