A filled function method for constrained global optimization
- Authors: Wu, Zhiyou , Bai, Fusheng , Lee, Heung , Yang, Yongjian
- Date: 2007
- Type: Text , Journal article
- Relation: Journal of Global Optimization Vol. 39, no. 4 (2007), p. 495-507
- Full Text: false
- Reviewed:
- Description: In this paper, a filled function method for solving constrained global optimization problems is proposed. A filled function is proposed for escaping the current local minimizer of a constrained global optimization problem by combining the idea of filled function in unconstrained global optimization and the idea of penalty function in constrained optimization. Then a filled function method for obtaining a global minimizer or an approximate global minimizer of the constrained global optimization problem is presented. Some numerical results demonstrate the efficiency of this global optimization method for solving constrained global optimization problems. © 2007 Springer Science+Business Media, Inc.
- Description: C1
- Description: 2003005513
An optimization approach to the study of drug-drug interactions
- Authors: Mammadov, Musa , Banerjee, Arunava
- Date: 2005
- Type: Text , Conference paper
- Relation: Paper pesented at Sixteenth Australasian Workshop on Combinatorial Algorithms, AWOCA 2005, Ballarat, Victoria : 18th-21st September 2005 p. 201-216
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- Description: Drug-drug interaction is one of the important problems of Adverse Drug Reaction (ADR). In this paper we develop an optimization approach for the study of this problem. This approach is based on drug-reaction relationships represented in the form of a vector of weights, which can be defined as a solution to some global optimization problem. Although this approach can be used for solving many ADR problems, we concentrate here only on drug-drug interactions. Based on drug-reaction relationships, we formulate this problem as an optimization problem. The approach is applied to different classes of reactions from the Australian Adverse Drug Reaction Advisory Committee (ADRAC) database.
- Description: 2003001384
An optimization approach to identifying drugs responsible for adverse drug reactions
- Authors: Mammadov, Musa , Banerjee, Arunava
- Date: 2005
- Type: Text , Conference paper
- Relation: Paper pesented at Sixteenth Australasian Workshop on Combinatorial Algorithms, AWOCA 2005, Ballarat, Victoria : 18th-21st September 2005 p. 185-200
- Full Text: false
- Description: In this paper we develop an optimization approach for the study of Adverse Drug Reaction (ADR) problems. This approach is based on drug-reaction relationships represented in the form of a vector weights, which can be defined as a solution to some global optimization problem. Although it can be used for solving many ADR problems, we concentrate on the problem of accurate identification of drugs that are responsible for reactions that have occurred. Based on drug-reaction relationships, we formulate this problem as an optimization problem. The approach is applied to Australian Adverse Drug Reaction Advisory Committee (ADRAC) database. We take a comprehensive approach to considering all reaction classes which combines 18 SOC (System Organ Class), as well as the sub-classes of reaction classes Blood, Body, Neurological and Cardiovascular. The numerical experiments provided high accuracy in prediction of suspected drugs reported in ADRAC database.
- Description: 2003001383
A heuristic algorithm for solving the minimum sum-of-squares clustering problems
- Authors: Ordin, Burak , Bagirov, Adil
- Date: 2015
- Type: Text , Journal article
- Relation: Journal of Global Optimization Vol. 61, no. 2 (2015), p. 341-361
- Relation: http://purl.org/au-research/grants/arc/DP140103213
- Full Text: false
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- Description: Clustering is an important task in data mining. It can be formulated as a global optimization problem which is challenging for existing global optimization techniques even in medium size data sets. Various heuristics were developed to solve the clustering problem. The global k-means and modified global k-means are among most efficient heuristics for solving the minimum sum-of-squares clustering problem. However, these algorithms are not always accurate in finding global or near global solutions to the clustering problem. In this paper, we introduce a new algorithm to improve the accuracy of the modified global k-means algorithm in finding global solutions. We use an auxiliary cluster problem to generate a set of initial points and apply the k-means algorithm starting from these points to find the global solution to the clustering problems. Numerical results on 16 real-world data sets clearly demonstrate the superiority of the proposed algorithm over the global and modified global k-means algorithms in finding global solutions to clustering problems.
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
- Full Text: false
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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 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
- Full Text: false
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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.
Solving the canonical dual of box-and integer-constrained nonconvex quadratic programs via a deterministic direct search algorithm
- Authors: Gao, David , Watson, Layne , Easterling, David , Thacker, William , Billups, Stephen
- Date: 2013
- Type: Text , Journal article
- Relation: Optimization Methods and Software Vol. 28, no. 2 (2013), p. 313-326
- Full Text: false
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- Description: This paper presents a massively parallel global deterministic direct search method (VTDIRECT) for solving nonconvex quadratic minimization problems with either box or1 integer constraints. Using the canonical dual transformation, these well-known NP-hard problems can be reformulated as perfect dual stationary problems (with zero duality gap). Under certain conditions, these dual problems are equivalent to smooth concave maximization over a convex feasible space. Based on a perturbation method proposed by Gao, the integer programming problem is shown to be equivalent to a continuous unconstrained Lipschitzian global optimization problem. The parallel algorithm VTDIRECT is then applied to solve these dual problems to obtain global minimizers. Parallel performance results for several nonconvex quadratic integer programming problems are reported. © 2013 Copyright Taylor and Francis Group, LLC.
- Description: 2003010580
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
- Full Text: false
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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 nonconvex optimization of 4th-order polynomial and log-sum-exp functions
- Authors: Chen, Yi , Gao, David
- Date: 2016
- Type: Text , Journal article
- Relation: Journal of Global Optimization Vol. 64, no. 3 (2016), p. 417-431
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- Description: This paper presents a canonical dual approach for solving a nonconvex global optimization problem governed by a sum of 4th-order polynomial and a log-sum-exp function. Such a problem arises extensively in engineering and sciences. Based on the canonical duality–triality theory, this nonconvex problem is transformed to an equivalent dual problem, which can be solved easily under certain conditions. We proved that both global minimizer and the biggest local extrema of the primal problem can be obtained analytically from the canonical dual solutions. As two special cases, a quartic polynomial minimization and a minimax problem are discussed. Existence conditions are derived, which can be used to classify easy and relative hard instances. Applications are illustrated by several nonconvex and nonsmooth examples. © 2014, Springer Science+Business Media New York.