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path following algorithm for matching partially overlapping feature sets

ELECTRONICS LETTERS 2015年第23期51卷 1863-1864页

作者： Lian, Wei Changzhi Univ Dept Comp Sci Changzhi 046011 Shanxi Peoples R China

To address feature matching problem where there is only partial overlap between the two feature sets, minimisation of an energy function consisting of feature matching costs and a concave regularisation term capable of handling partial overlaps is proposed. To improve robustness to disturbances, a path following strategy for minimisation which dynamically combines weights of the two terms is adopted. Experimental results verify better performance of the method over several state-of-the-art methods.

关键词： feature extraction image matching set theory concave regularisation energy function feature matching problem partially overlapping feature sets path following algorithm robustness

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A polynomial path following algorithm for convex programming

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APPLIED MATHEMATICS AND COMPUTATION 2008年第2期196卷 866-878页

作者： Fan, Xiaona Yu, Bo Dalian Univ Technol Dept Appl Math Dalian 116024 Peoples R China

In this paper, based on combined homotopy interior point method we propose an interior point algorithm for convex nonlinear programming. The algorithm ensures that the obtained iterative points are interior points of the feasible set in terms of the technique of beta-cone neighborhood. We establish the global convergence of the algorithm. Furthermore, it is shown that the algorithm has O(root nL) iteration complexity. The preliminary numerical experiments indicate that the algorithm is efficient. (C) 2007 Elsevier Inc. All rights reserved.

关键词： convex nonlinear programming combined homotopy path following algorithm global convergence polynomial-time algorithm

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An Extended path following algorithm for Graph-Matching Problem

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IEEE TRANSACTIONS ON PATTERN ANALYSIS AND MACHINE INTELLIGENCE 2012年第7期34卷 1451-1456页

作者： Liu, Zhi-Yong Qiao, Hong Xu, Lei Chinese Acad Sci State Key Lab Management & Control Complex Syst Inst Automat Beijing 100190 Peoples R China Chinese Univ Hong Kong Dept Comp Sci & Engn Shatin Hong Kong Peoples R China

The path following algorithm was proposed recently to approximately solve the matching problems on undirected graph models and exhibited a state-of-the-art performance on matching accuracy. In this paper, we extend the path following algorithm to the matching problems on directed graph models by proposing a concave relaxation for the problem. Based on the concave and convex relaxations, a series of objective functions are constructed, and the Frank-Wolfe algorithm is then utilized to minimize them. Several experiments on synthetic and real data witness the validity of the extended path following algorithm.

关键词： Graph matching convex relaxation concave relaxation directed graph path following algorithm

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New path following algorithm for Convex Programming

New Path Following Algorithm for Convex Programming

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4th International Conference on Information Computing and Applications (ICICA)

作者： Fan, Xiaona Gong, Dianxuan Nanjing Univ Posts & Telecommun Coll Sci Nanjing 210046 Jiangsu Peoples R China Hebei United Univ Coll Sci Tangshan 063009 Peoples R China

ISBN: (纸本)9783642537035;9783642537028

To study a path following algorithm for tracing a constraint shifting combined homogony method for convex nonlinear programming. The method is based on the technique of beta -cone neighbourhood which ensures the obtained iterative points are in the interior of the constraint shifting feasible set. To establish the global linear convergence of the algorithm the numerical experiments indicate that the algorithm is efficient.

关键词： Convex Nonlinear Programming Constraint Shifting Combined Homogony path following algorithm Global Convergence

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The global linear convergence of a noninterior path-following algorithm for linear complementarity problems

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MATHEMATICS OF OPERATIONS RESEARCH 1998年第3期23卷 719-734页

作者： Burke, JV Xu, S Univ Washington Dept Math Seattle WA 98195 USA

A noninterior path-following algorithm is proposed for the linear complementarity problem. The method employs smoothing techniques introduced by Kanzow. If the LCP is P-0 + R-0 and satisfies a nondegeneracy condition due to Fukushima, Luo, and Pang, then the algorithm is globally linearly convergent. As with interior point path-following methods, the convergence theory relies on the notion of a neighborhood for the central path. However, the choice of neighborhood differs significantly from that which appears in the interior point literature. Numerical experiments are presented that illustrate the significance of the neighborhood concept for this class of methods.

关键词： linear complementarity problem noninterior algorithm path following algorithm interior point algorithm global linear convergence

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Smart carrot chasing guidance law for path following of unmanned surface vehicles

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PROCEEDINGS OF THE INSTITUTION OF MECHANICAL ENGINEERS PART M-JOURNAL OF ENGINEERING FOR THE MARITIME ENVIRONMENT 2024年第3期238卷 567-576页

作者： Unal, Osman Akkas, Nuri Atali, Gokhan Ozkan, Sinan Serdar Sakarya Univ Appl Sci Dept Mech Engn Sakarya Turkiye Sakarya Univ Appl Sci Dept Mechatron Engn Sakarya Turkiye Sakarya Univ Appl Sci Dept Mech Engn TR-54050 Serdivan Sakarya Turkiye

Carrot chasing guidance law is one of the most widely used path following algorithms due to its simplicity and ease of implementation;however, it has a fixed parameter which leads to large cross-tracking errors during different navigational conditions. This study proposes an innovative approach to carrot chasing algorithm to minimize cross-tracking errors. Pattern search optimization technique is integrated with carrot chasing guidance law to determine unique virtual target points obtained by flexible parameters instead of a fixed parameter. Proposed smart carrot chasing guidance law (SCCGL) provides stable and accurate path following even for different navigational conditions of unmanned surface vehicle (USV). To the best of our knowledge, we are the first to apply pattern search optimization technique to carrot chasing guidance law while USV is performing multi-tasks of predefined paths. This novelty significantly reduces both cross tracking errors and computational costs. Firstly, SCCGL is tested and compared with traditional carrot chasing algorithm in the numerical simulator for several navigational conditions such as different lists of waypoints, different initial locations, and different maximum turning rates of USV. SCCGL automatically determines optimal parameters to make stable and accurate navigation. SCCGL significantly reduces cross tracking errors compared to classical carrot chasing algorithm. This is the first contribution of this paper. Secondly, genetic algorithm optimization method has been implemented to carrot chasing guidance law instead of pattern search optimization technique. Genetic algorithm causes the total simulation time to be quite long. The proposed SCCGL (pattern search integrated carrot chasing guidance law) gives optimum results 20 times faster than the genetic algorithm. This is the second and main contribution of developed SCCGL method. It is observed that SCCGL provides best navigation with minimum cross-tracking errors and mini

关键词： path following algorithm carrot-chasing guidance law pattern search algorithm cross-tracking error unmanned surface vehicle

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A globally convergent interior point algorithm for non-convex nonlinear programming

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JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS 2009年第2期224卷 622-627页

作者： Fan, Xiaona Nanjing Univ Posts & Telecommun Coll Math & Phys Nanjing 210046 Jiangsu Peoples R China

in this paper, a new algorithm for tracing the combined homotopy path of the non-convex nonlinear programming problem is proposed. The algorithm is based on the techniques of beta-cone neighborhood and a combined homotopy interior point method. The residual control criteria, which ensures that the obtained iterative points are interior points, is given by the condition that ensures the beta-cone neighborhood to be included in the interior part of the feasible region. The global convergence and polynomial complexity are established under some hypotheses. (c) 2008 Elsevier B.V. All rights reserved.

关键词： Non-convex programming Combined interior homotopy path following algorithm Global convergence

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An algorithm constructing solutions for a family of linear semi-infinite problems

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JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS 2001年第3期110卷 585-609页

作者： Kostyukova, OI Byelarussian Acad Sci Inst Math Minsk BELARUS

A family of linear semi-infinite problems depending on a parameter tau epsilon= [0, tau*] is considered. For fixed tau = tau (0)epsilon [0, omega*], a sensitivity analysis of the problem solution is carried out and rules constructing the solutions of this family for tau in a right-side neighborhood of tau (0) are described. Results on the one-sided derivatives of the solution with respect to the parameter are presented. On the basis of the results, an active-set-strategy and a path-following algorithm are suggested.

关键词： semi-infinite programming parametric programming path following algorithm active-set strategy

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Incremental learning algorithm for large-scale semi-supervised ordinal regression

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NEURAL NETWORKS 2022年第0期149卷 124-136页

作者： Chen, Haiyan Jia, Yizhen Ge, Jiaming Gu, Bin Nanjing Univ Aeronaut & Astronaut Coll Comp Sci & Technol Nanjing 210006 Peoples R China Nanjing Univ Informat Sci & Technol Coll Comp & Software Nanjing 210006 Peoples R China

As a special case of multi-classification, ordinal regression (also known as ordinal classification) is a popular method to tackle the multi-class problems with samples marked by a set of ranks. Semi supervised ordinal regression (SSOR) is especially important for data mining applications because semi-supervised learning can make use of the unlabeled samples to train a high-quality learning model. However, the training of large-scale SSOR is still an open question due to its complicated formulations and non-convexity to the best of our knowledge. To address this challenging problem, in this paper, we propose an incremental learning algorithm for SSOR (IL-SSOR), which can directly update the solution of SSOR based on the KKT conditions. More critically, we analyze the finite convergence of IL-SSOR which guarantees that SSOR can converge to a local minimum based on the framework of concave-convex procedure. To the best of our knowledge, the proposed new algorithm is the first efficient on-line learning algorithm for SSOR with local minimum convergence guarantee. The experimental results show, IL-SSOR can achieve better generalization than other semi-supervised multi-class algorithms. Compared with other semi-supervised ordinal regression algorithms, our experimental results show that IL-SSOR can achieve similar generalization with less running time. (C) 2022 Elsevier Ltd. All rights reserved.

关键词： Semi-supervised ordinal regression Incremental learning Concave-Convex procedure algorithm path following algorithm

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ELLIPSOIDS THAT CONTAIN ALL THE SOLUTIONS OF A POSITIVE SEMIDEFINITE LINEAR COMPLEMENTARITY-PROBLEM

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MATHEMATICAL PROGRAMMING 1990年第3期48卷 415-435页

作者： KOJIMA, M MIZUNO, S YOSHISE, A TOKYO INST TECHNOL DEPT IND ENGN & MANAGEMENTTOKYO 152JAPAN

This paper deals with the LCP (linear complementarity problem) with a positive semi-definite matrix. Assuming that a strictly positive feasible solution of the LCP is available, we propose ellipsoids each of which contains all the solutions of the LCP. We use such an ellipsoid for computing a lower bound and an upper bound for each coordinate of the solutions of the LCP. We can apply the lower bound to test whether a given variable is positive over the solution set of the LCP. That is, if the lower bound is positive, we know that the variable is positive over the solution set of the LCP; hence, by the complementarity condition, its complement is zero. In this case we can eliminate the variable and its complement from the LCP. We also show how we efficiently combine the ellipsoid method for computing bounds for the solution set with the path-following algorithm proposed by the authors for the LCP. If the LCP has a unique non-degenerate solution, the lower bound and the upper bound for the solution, computed at each iteration of the path-following algorithm, both converge to the solution of the LCP.

关键词： Linear complementarity problem ellipsoid interior point algorithm path following algorithm

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