EDP Sciences logo
Subscriber Authentication Point
Search
Menu
All issues Volume 55 / No 6 (November-December 2021) RAIRO-Oper. Res., 55 6 (2021) 3743-3771 References
Open Access
Issue
RAIRO-Oper. Res.
Volume 55, Number 6, November-December 2021
Page(s) 3743 - 3771
DOI https://doi.org/10.1051/ro/2021179
Published online 17 December 2021
  • E.G. Birgin, C. Floudas and J.M. Martnez, Global minimization using an Augmented Lagrangian method with variable lower-level constraints. Math. Program. 125 (2010) 139–162. [CrossRef] [MathSciNet] [Google Scholar]
  • M.J. Cloud, R.E. Moore and R.B. Kearfott, Introduction to Interval Analysis. Siam, Philadelphia (2009). [Google Scholar]
  • C. De Boor, On Calculating with B-splines. J. Approximation Theory 6 (1972) 50–62. [CrossRef] [MathSciNet] [Google Scholar]
  • C.A. Floudas and P.M. Pardalos, A Collection of Test Problems for Constrained Global Optimization Algorithms. Vol. 455. Springer (1990). [CrossRef] [Google Scholar]
  • C.A. Floudas, P.M. Pardalos, C. Adjiman, W.R. Esposito, Z.H. Gümüs, S.T. Harding, J.L. Klepeis, C.A. Meyer and C.A. Schweiger, Handbook of Test Problems in Local and Global Optimization. Springer Science & Business Media (2013). [Google Scholar]
  • J. Garloff, The Bernstein algorithm. Interval Comput. 6 (1993) 154–168. [Google Scholar]
  • D.D. Gawali, A. Zidna and P.S.V. Nataraj, Solving nonconvex optimization problems in systems and control: a polynomial B-spline approach. In: Modelling, Computation and Optimization in Information Systems and Management Sciences. Springer (2015) 467–478. [Google Scholar]
  • D.D. Gawali, A. Zidna and P.S.V. Nataraj, Algorithms for unconstrained global optimization of nonlinear (polynomial) programming problems: the single and multi-segment polynomial B-spline approach. Comput. Oper. Res. 87 (2017) 205–220. [CrossRef] [MathSciNet] [Google Scholar]
  • D.D. Gawali, B.V. Patil, A. Zidna and P.S.V. Nataraj, A B-spline global optimization algorithm for optimal power flow problem. In: World Congress on Global Optimization. Springer (2019) 58–67. [Google Scholar]
  • Global library. available online at http://www.gamsworld.org/global/globallib. [Google Scholar]
  • B. Grimstad, A MIQCP formulation for B-spline constraints. Optim. Lett. 12 (2018) 713–725. [CrossRef] [MathSciNet] [Google Scholar]
  • B. Grimstad and B.R. Knudsen, Mathematical programming formulations for piecewise polynomial functions. J. Global Optim. 77 (2020) 455–486. [CrossRef] [MathSciNet] [Google Scholar]
  • B. Grimstad and A. Sandnes, Global optimization with spline constraints: a new branch-and-bound method based on B-splines. J. Global Optim. 65 (2016) 401–439. [CrossRef] [MathSciNet] [Google Scholar]
  • E. Hansen and G. Walster, Global Optimization Using Interval Analysis, 2nd edition. Revised and Expanded. Vol. 264, Marcel DEKKER, INC., New York (2004). [Google Scholar]
  • D. Henrion and J.B. Lasserre, Gloptipoly: global optimization over polynomials with matlab and sedumi. ACM Trans. Math. Softw. (TOMS) 29 (2003) 165–194. [CrossRef] [Google Scholar]
  • D. Henrion and J.B. Lasserre, Solving nonconvex optimization problems. IEEE Control Syst. Mag. 24 (2004) 72–83. [CrossRef] [Google Scholar]
  • R. Horst and P.M. Pardalos, Handbook of Global Optimization. Kluwer Academic Publishers, Dordrecht, The Netherlands (1995). [CrossRef] [Google Scholar]
  • L. Jaulin, Applied Interval Analysis: With Examples in Parameter and State Estimation, Robust Control and Robotics. Vol. 1. Springer Science & Business Media (2001). [Google Scholar]
  • R.B. Kearfott, Rigorous Global Search: Continuous Problems. Vol. 13, Springer Science & Business Media (2013). [Google Scholar]
  • J.B. Lasserre, Global optimization with polynomials and the problem of moments. SIAM J. Optim. 11 (2001) 796–817. [Google Scholar]
  • Q. Lin and J. Rokne, Methods for bounding the range of a polynomial. J. Comput. Appl. Math. 58 (1995) 193–199. [CrossRef] [MathSciNet] [Google Scholar]
  • Q. Lin and J. Rokne, Interval approximation of higher order to the ranges of functions. Comput. Math. App. 31 (1996) 101–109. [Google Scholar]
  • T. Lyche and K. Morken, Spline Methods Draft. Department of Informatics, Centre of Mathematics for Applications, University of Oslo (2008). [Google Scholar]
  • Mathworks Inc., MATLAB version 8.0.0.783 (R 2012 b), Inc. Natick, Massachusetts, United States (2012). [Google Scholar]
  • D. Michel, H. Mraoui, D. Sbibih and A. Zidna, Computing the range of values of real functions using B-spline form. Appl. Math. Comput. 233 (2014) 85–102. [MathSciNet] [Google Scholar]
  • P.S.V. Nataraj and M. Arounassalame, An algorithm for constrained global optimization of multivariate polynomials using the Bernstein form and John optimality conditions. Opsearch 46 (2009) 133–152. [CrossRef] [MathSciNet] [Google Scholar]
  • P.S.V. Nataraj and M. Arounassalame, Constrained global optimization of multivariate polynomials using Bernstein branch and prune algorithm. J. Global Optim. 49 (2011) 185–212. [CrossRef] [MathSciNet] [Google Scholar]
  • NEOS Server for optimization. http://www.neos-server.org/neos/solvers/ (2018). [Google Scholar]
  • S. Park, Approximate branch-and-bound global optimization using B-spline hypervolumes. Adv. Eng. Softw. 45 (2012) 11–20. [CrossRef] [Google Scholar]
  • B.V. Patil, Global optimization of polynomial mixed-integer nonlinear problems using the Bernstein form. Ph.D. thesis. Indian Institute of Technology, Bombay (2012). [Google Scholar]
  • B.V. Patil, P.S.V. Nataraj and S. Bhartiya, Global optimization of mixed-integer nonlinear (polynomial) programming problems: the bernstein polynomial approach. Computing 94 (2012) 325–343. [CrossRef] [MathSciNet] [Google Scholar]
  • H. Ratschek and J. Rokne, Computer Methods for the Range of Functions. Ellis Horwood Limited, Chichester, England (1984). [Google Scholar]
  • H. Ratschek and J. Rokne, New Computer Methods for Global Optimization. Ellis Horwood Limited, Chichester, England (1988). [Google Scholar]
  • C.K. Shene, CS3621 Introduction to computing with geometry notes. http://www.cs.mtu.edu/shene/COURSES/cs3621/NOTES/ (2014). [Google Scholar]
  • R. Vaidyanathan and M. El-Halwagi, Global optimization of nonconvex nonlinear programs via interval analysis. Comput. Chem. Eng. 18 (1994) 889–897. [CrossRef] [Google Scholar]
  • P. Van Hentenryck, D. McAllester and D. Kapur, Solving polynomial systems using a branch and prune approach. SIAM J. Numer. Anal. 34 (1997) 797–827. [CrossRef] [MathSciNet] [Google Scholar]

Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.

Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.

Initial download of the metrics may take a while.