A parametric solution algorithm for a class of rank-two nonconvex programs

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• 作者：Riccardo Cambini (1)
  Claudio Sodini (1)
  
• 关键词：Nonconvex programs ; Low ; rank programs ; Quadratic programs ; Global optimization ; C61 ; C63
• 刊名：Journal of Global Optimization
• 出版年：2014
• 出版时间：December 2014
• 年：2014
• 卷：60
• 期：4
• 页码：649-662
• 全文大小：193 KB
• 参考文献：1. Cambini, A., Martein, L.: Generalized Convexity and Optimization: Theory and applications. Lecture Notes in Economics and Mathematical Systems, vol. 616. Springer, Berlin (2009)
  2. Cambini, R., Sodini, C.: A finite algorithm for a class of nonlinear multiplicative programs. J. Global Optim. 26, 279-96 (2003) CrossRef
  3. Cambini, R., Sodini, C.: Global optimization of a rank-two nonconvex program. Math. Methods Oper. Res. 71, 165-80 (2010) CrossRef
  4. Cambini, R., Sodini, C.: A unifying approach to solve some classes of rank-three multiplicative and fractional programs involving linear functions. Eur. J. Oper. Res. 207, 25-9 (2010) CrossRef
  5. Cambini, R., Sodini, C.: A parametric approach for solving a class of generalized quadratic-transformable rank-two nonconvex programs. J. Comput. Appl. Math. 236, 2685-695 (2012) CrossRef
  6. Ellero, A.: The optimal level solutions method. J. Inf. Optim. Sci. 17, 355-72 (1996)
  7. Hadjisavvas, N., Komlósi, S., Schaible, S. (eds.): Handbook of Generalized Convexity and Generalized Monotonicity, Nonconvex Optimization and Its Applications, 76. Springer, New York (2005)
  8. Horst, R., Pardalos, P.M. (eds.): Handbook of Global Optimization, Nonconvex Optimization and Its Applications, 2. Kluwer, Dordrecht (1995)
  
• 作者单位：Riccardo Cambini (1)
  Claudio Sodini (1)
  
  1. Department of Economics and Management, University of Pisa, Via Cosimo Ridolfi 10, 56124?, Pisa, Italy
  
• ISSN：1573-2916

文摘

The aim of this paper is to propose a solution algorithm for a particular class of rank-two nonconvex programs having a polyhedral feasible region. The algorithm lies within the class of the so called “optimal level solutions-parametric methods. The subproblems obtained by means of this parametrical approach are quadratic convex ones, but not necessarily neither strictly convex nor linear. For this very reason, in order to solve in an unifying framework all of the considered rank-two nonconvex programs a new approach needs to be proposed. The efficiency of the algorithm is improved by means of the use of underestimation functions. The results of a computational test are provided and discussed.