Ning Ruan

Global optimal solutions to general sensor network localization problem

Abstract Sensor network localization problem is to determine the position of the sensor nodes in a network given pairwise distance measurements. Such problem can be formulated as a quartic polynomial minimization via the least squares method. This paper presents a canonical duality theory for solving this challenging problem. It is shown that the nonconvex minimization problem can be reformulated as a concave maximization dual problem over a convex set in a symmetrical matrix space, and hence can be solved efficiently by combining a general (linear or quadratic) perturbation technique with existing optimization techniques. Applications are illustrated by solving some relatively large-scale problems. Our results show that the general sensor network localization problem is not NP-hard unless its canonical dual problem has no solution in its positive definite domain. Fundamental ideas for solving general NP-hard problems are discussed.

RETRACTED: Canonical duality–triality theory: bridge between nonconvex analysis/mechanics and global optimization in complex systems

The following article has been included in a multiple retraction: Canonical Duality-Triality theory: Bridge between Nonconvex Analysis/Mechanics and Global Optimization in complex systems; David Y Gao, Ning Ruan, and Vittorio Latorre. http://mms.sagepub.com/content/early/2015/02/24/1081286514566533.abstract In 2015 SAGE were made aware of concerns regarding the Special Issue of Mathematics & Mechanics of Solids on Advances in Canonical Duality Theory, guest-edited by Professor David Gao. At the request of the Guest Editor, the Special Issue has been retracted, due to conflict of interest regarding Professor Gao’s role as Guest Editor and co-author on a number of submitted papers. In addition the peer review process was less rigorous than the journal requires. The Guest Editor takes full responsibility for the retraction. The following articles that were due to appear in the Special Issue have therefore been retracted: Canonical Duality-Triality: Bridge between Nonconvex Analysis/Mechanics and Global Optimization in complex systems; David Y Gao, Ning Ruan, and Vittorio Latorre. http://mms.sagepub.com/content/early/2015/02/24/1081286514566533.abstract Canonical Dual Approach for Contact Mechanics Problems with Friction; Vittorio Latorre, Simone Sagratella, David Y Gao. http://mms.sagepub.com/content/early/2015/01/20/1081286514566534.abstract Canonical Duality Theory for Solving Non-Monotone Variational Inequality Problems; Guoshan Liu, David Y Gao, Shouyang Wang. http://mms.sagepub.com/content/early/2015/02/04/1081286514566535.abstract Double Well Potential Function and Its Optimization in The n-dimensional Real Space. Part I; Shu-Cherng Fang, David Y Gao, Gang-Xuan Lin, Ruey-Lin Sheu, Wen-Xun Xing. http://mms.sagepub.com/content/early/2015/02/24/1081286514566704.abstract Double Well Potential Function and Its Optimization in The n-dimensional Real Space. Part II; Yong Xia, Ruey-Lin Sheu, Shu-Cherng Fang, Wenxun Xing. http://mms.sagepub.com/content/early/2015/02/09/1081286514566723.abstract Analytic Solutions to 3-D Finite Deformation Problems Governed by St Venant-Kirchhoff Material; David Y Gao and E. Hajilarov. http://mms.sagepub.com/content/early/2015/07/06/1081286515591084.abstract Triality Theory and Complete Post-buckling Solutions of Large Deformed Beam by Canonical Dual Finite Element Method; Kun Cai, David Y Gao, Qinghua Qin. http://mms.sagepub.com/content/early/2015/06/28/1081286515591085.abstract Global Solutions to Spherically Constrained Quadratic Minimization via Canonical Duality Theory; Yi Chen, David Y Gao. http://mms.sagepub.com/content/early/2015/04/08/1081286515577122.abstract Unified Canonical Duality Methodology for Global Optimization; Vittorio Latorre, David Y Gao and N. Ruan. http://mms.sagepub.com/content/early/2015/07/06/1081286515591305.abstract A Framework of Canonical Dual Algorithms for Global Optimization; Xiaojun Zhou, David Y Gao, Chunhua Yang. http://mms.sagepub.com/content/early/2015/07/22/1081286515592190.abstract Canonical Duality Theory for Solving Nonconvex/Discrete Constrained Global Optimization Problems; Ning Ruan, David Y Gao. http://mms.sagepub.com/content/early/2015/07/08/1081286515591087.abstract Global Optimization Solutions to a Class of Non-convex Quadratic Minimization Problems with Quadratic Constraints; Yubo Yuan. http://mms.sagepub.com/content/early/2015/07/06/1081286515591086.abstract On Minimal Distance between Two Non-Convex Surfaces; Daniel Morales-Silva, David Y Gao. http://mms.sagepub.com/content/early/2015/07/27/1081286515592949.abstract The Editor-in-Chief and SAGE strive to uphold the very highest standards of publication ethics and are committed to supporting the high standards of integrity of Mathematics & Mechanics of Solids. Authors, reviewers, editors and interested readers are encouraged to consult SAGE’s ethics statements and the Committee on Publication Ethics (COPE) website for guidelines on publication ethics.

Global solutions to fractional programming problem with ratio of nonconvex functions

This paper presents a canonical dual approach for minimizing a sum of quadratic function and a ratio of nonconvex functions in R n . By introducing a parameter, the problem is first equivalently reformed as a nonconvex polynomial minimization with elliptic constraint. It is proved that under certain conditions, the canonical dual is a concave maximization problem in R 2 that exhibits no duality gap. Therefore, the global optimal solution of the primal problem can be obtained by solving the canonical dual problem.

Global Optimal Solution to Quadratic Discrete Programming Problem with Inequality Constraints

This paper presents a canonical dual method for solving a quadratic discrete value selection problem subjected to inequality constraints. By using a linear transformation, the problem is first reformulated as a standard quadratic 0–1 integer programming problem. Then, by the canonical duality theory, this challenging problem is converted to a concave maximization over a convex feasible set in continuous space. It is proved that if this canonical dual problem has a solution in its feasible space, the corresponding global solution to the primal problem can be obtained directly by a general analytical form. Otherwise, the problem could be NP-hard. In this case, a quadratic perturbation method and an associated canonical primal-dual algorithm are proposed. Numerical examples are illustrated to demonstrate the efficiency of the proposed method and algorithm.

RETRACTED: Unified canonical duality methodology for global optimization

The following article has been included in a multiple retraction: Unified Canonical Duality Methodology for Global Optimization; Vittorio Latorre, David Y Gao and N. Ruan. http://mms.sagepub.com/content/early/2015/07/06/1081286515591305.abstract In 2015 SAGE were made aware of concerns regarding the Special Issue of Mathematics & Mechanics of Solids on Advances in Canonical Duality Theory, guest-edited by Professor David Gao. At the request of the Guest Editor, the Special Issue has been retracted, due to conflict of interest regarding Professor Gao’s role as Guest Editor and co-author on a number of submitted papers. In addition the peer review process was less rigorous than the journal requires. The Guest Editor takes full responsibility for the retraction. The following articles that were due to appear in the Special Issue have therefore been retracted: Canonical Duality-Triality: Bridge between Nonconvex Analysis/Mechanics and Global Optimization in complex systems; David Y Gao, Ning Ruan, and Vittorio Latorre. http://mms.sagepub.com/content/early/2015/02/24/1081286514566533.abstract Canonical Dual Approach for Contact Mechanics Problems with Friction; Vittorio Latorre, Simone Sagratella, David Y Gao. http://mms.sagepub.com/content/early/2015/01/20/1081286514566534.abstract Canonical Duality Theory for Solving Non-Monotone Variational Inequality Problems; Guoshan Liu, David Y Gao, Shouyang Wang. http://mms.sagepub.com/content/early/2015/02/04/1081286514566535.abstract Double Well Potential Function and Its Optimization in The n-dimensional Real Space. Part I; Shu-Cherng Fang, David Y Gao, Gang-Xuan Lin, Ruey-Lin Sheu, Wen-Xun Xing. http://mms.sagepub.com/content/early/2015/02/24/1081286514566704.abstract Double Well Potential Function and Its Optimization in The n-dimensional Real Space. Part II; Yong Xia, Ruey-Lin Sheu, Shu-Cherng Fang, Wenxun Xing. http://mms.sagepub.com/content/early/2015/02/09/1081286514566723.abstract Analytic Solutions to 3-D Finite Deformation Problems Governed by St Venant-Kirchhoff Material; David Y Gao and E. Hajilarov. http://mms.sagepub.com/content/early/2015/07/06/1081286515591084.abstract Triality Theory and Complete Post-buckling Solutions of Large Deformed Beam by Canonical Dual Finite Element Method; Kun Cai, David Y Gao, Qinghua Qin. http://mms.sagepub.com/content/early/2015/06/28/1081286515591085.abstract Global Solutions to Spherically Constrained Quadratic Minimization via Canonical Duality Theory; Yi Chen, David Y Gao. http://mms.sagepub.com/content/early/2015/04/08/1081286515577122.abstract Unified Canonical Duality Methodology for Global Optimization; Vittorio Latorre, David Y Gao and N. Ruan. http://mms.sagepub.com/content/early/2015/07/06/1081286515591305.abstract A Framework of Canonical Dual Algorithms for Global Optimization; Xiaojun Zhou, David Y Gao, Chunhua Yang. http://mms.sagepub.com/content/early/2015/07/22/1081286515592190.abstract Canonical Duality Theory for Solving Nonconvex/Discrete Constrained Global Optimization Problems; Ning Ruan, David Y Gao. http://mms.sagepub.com/content/early/2015/07/08/1081286515591087.abstract Global Optimization Solutions to a Class of Non-convex Quadratic Minimization Problems with Quadratic Constraints; Yubo Yuan. http://mms.sagepub.com/content/early/2015/07/06/1081286515591086.abstract On Minimal Distance between Two Non-Convex Surfaces; Daniel Morales-Silva, David Y Gao. http://mms.sagepub.com/content/early/2015/07/27/1081286515592949.abstract The Editor-in-Chief and SAGE strive to uphold the very highest standards of publication ethics and are committed to supporting the high standards of integrity of Mathematics & Mechanics of Solids. Authors, reviewers, editors and interested readers are encouraged to consult SAGE’s ethics statements and the Committee on Publication Ethics (COPE) website for guidelines on publication ethics.

RETRACTED: Canonical duality theory for solving nonconvex/discrete constrained global optimization problems

The following article has been included in a multiple retraction: Canonical Duality Theory for Solving Nonconvex/Discrete Constrained Global Optimization Problems; Ning Ruan, David Y Gao. http://mms.sagepub.com/content/early/2015/07/08/1081286515591087.abstract In 2015 SAGE were made aware of concerns regarding the Special Issue of Mathematics & Mechanics of Solids on Advances in Canonical Duality Theory, guest-edited by Professor David Gao. At the request of the Guest Editor, the Special Issue has been retracted, due to conflict of interest regarding Professor Gao’s role as Guest Editor and co-author on a number of submitted papers. In addition the peer review process was less rigorous than the journal requires. The Guest Editor takes full responsibility for the retraction. The following articles that were due to appear in the Special Issue have therefore been retracted: Canonical Duality-Triality: Bridge between Nonconvex Analysis/Mechanics and Global Optimization in complex systems; David Y Gao, Ning Ruan, and Vittorio Latorre. http://mms.sagepub.com/content/early/2015/02/24/1081286514566533.abstract Canonical Dual Approach for Contact Mechanics Problems with Friction; Vittorio Latorre, Simone Sagratella, David Y Gao. http://mms.sagepub.com/content/early/2015/01/20/1081286514566534.abstract Canonical Duality Theory for Solving Non-Monotone Variational Inequality Problems; Guoshan Liu, David Y Gao, Shouyang Wang. http://mms.sagepub.com/content/early/2015/02/04/1081286514566535.abstract Double Well Potential Function and Its Optimization in The n-dimensional Real Space. Part I; Shu-Cherng Fang, David Y Gao, Gang-Xuan Lin, Ruey-Lin Sheu, Wen-Xun Xing. http://mms.sagepub.com/content/early/2015/02/24/1081286514566704.abstract Double Well Potential Function and Its Optimization in The n-dimensional Real Space. Part II; Yong Xia, Ruey-Lin Sheu, Shu-Cherng Fang, Wenxun Xing. http://mms.sagepub.com/content/early/2015/02/09/1081286514566723.abstract Analytic Solutions to 3-D Finite Deformation Problems Governed by St Venant-Kirchhoff Material; David Y Gao and E. Hajilarov. http://mms.sagepub.com/content/early/2015/07/06/1081286515591084.abstract Triality Theory and Complete Post-buckling Solutions of Large Deformed Beam by Canonical Dual Finite Element Method; Kun Cai, David Y Gao, Qinghua Qin. http://mms.sagepub.com/content/early/2015/06/28/1081286515591085.abstract Global Solutions to Spherically Constrained Quadratic Minimization via Canonical Duality Theory; Yi Chen, David Y Gao. http://mms.sagepub.com/content/early/2015/04/08/1081286515577122.abstract Unified Canonical Duality Methodology for Global Optimization; Vittorio Latorre, David Y Gao and N. Ruan. http://mms.sagepub.com/content/early/2015/07/06/1081286515591305.abstract A Framework of Canonical Dual Algorithms for Global Optimization; Xiaojun Zhou, David Y Gao, Chunhua Yang. http://mms.sagepub.com/content/early/2015/07/22/1081286515592190.abstract Canonical Duality Theory for Solving Nonconvex/Discrete Constrained Global Optimization Problems; Ning Ruan, David Y Gao. http://mms.sagepub.com/content/early/2015/07/08/1081286515591087.abstract Global Optimization Solutions to a Class of Non-convex Quadratic Minimization Problems with Quadratic Constraints; Yubo Yuan. http://mms.sagepub.com/content/early/2015/07/06/1081286515591086.abstract On Minimal Distance between Two Non-Convex Surfaces; Daniel Morales-Silva, David Y Gao. http://mms.sagepub.com/content/early/2015/07/27/1081286515592949.abstract The Editor-in-Chief and SAGE strive to uphold the very highest standards of publication ethics and are committed to supporting the high standards of integrity of Mathematics & Mechanics of Solids. Authors, reviewers, editors and interested readers are encouraged to consult SAGE’s ethics statements and the Committee on Publication Ethics (COPE) website for guidelines on publication ethics.

Application of Canonical Duality Theory to Fixed Point Problem

In this paper, we study general fixed point problem. We first rewrite the original problem in the canonical framework. Then, we proposed a canonical transformation of this problem, which leads to a convex differentiable dual problem and new iteration method. An illustrative example is presented.

Canonical duality theory and algorithm for solving challenging problems in network optimisation

This paper presents a canonical dual approach for solving a general nonconvex problem in network optimization. Three challenging problems, sensor network location, traveling salesman problem, and scheduling problem are listed to illustrate the applications of the proposed method. It is shown that by the canonical duality, these nonconvex and integer optimization problems are equivalent to unified concave maximization problem over a convex set and hence can be solved efficiently by existing optimization techniques.