McCormick-Based Relaxations of Algorithms

作者: Benoit Chachuat , Alexander Mitsos , Paul I. Barton

DOI:

关键词: Function (mathematics)Differential equationBasis (linear algebra)MathematicsAffine transformationRelaxation (approximation)AlgorithmGlobal optimizationBoundary (topology)Subgradient method

摘要: … relaxations of factorable functions by McCormick [Math. Prog., 10 (1976), pp. 147–175]. … for any factorable function for which a McCormick relaxation exists, provided that subgradients …

参考文章(15)
Adam Benjamin Singer, Global Dynamic Optimization Massachusetts Institute of Technology. ,(2004)
Xiaojun Wang, Tsu-Shuan Chang, A Multivariate Global Optimization Using Linear Bounding Functions Journal of Global Optimization. ,vol. 12, pp. 383- 404 ,(1998) , 10.1023/A:1008229430888
Jean-Baptiste Hiriart-Urruty, Claude Lemaréchal, Convex analysis and minimization algorithms ,(1993)
R.P. Byrne, I.D.L. Bogle, Global optimisation of constrained non-convex programs using reformulation and interval analysis Computers & Chemical Engineering. ,vol. 23, pp. 1341- 1350 ,(1999) , 10.1016/S0098-1354(99)00295-1
Mohit Tawarmalani, Nikolaos V. Sahinidis, A polyhedral branch-and-cut approach to global optimization Mathematical Programming. ,vol. 103, pp. 225- 249 ,(2005) , 10.1007/S10107-005-0581-8
Benoît Chachuat, Adam B. Singer, Paul I. Barton, Global methods for dynamic optimization and mixed-integer dynamic optimization Industrial & Engineering Chemistry Research. ,vol. 45, pp. 8373- 8392 ,(2006) , 10.1021/IE0601605
Padmanaban Kesavan, Paul I. Barton, Generalized branch-and-cut framework for mixed-integer nonlinear optimization problems Computers & Chemical Engineering. ,vol. 24, pp. 1361- 1366 ,(2000) , 10.1016/S0098-1354(00)00421-X
E.M.B. Smith, C.C. Pantelides, A symbolic reformulation/spatial branch-and-bound algorithm for the global optimisation of nonconvex MINLPs Computers & Chemical Engineering. ,vol. 23, pp. 457- 478 ,(1999) , 10.1016/S0098-1354(98)00286-5
John Tolsma, Paul I. Barton, DAEPACK: An Open Modeling Environment for Legacy Models Industrial & Engineering Chemistry Research. ,vol. 39, pp. 1826- 1839 ,(2000) , 10.1021/IE990734O