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. [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. [Google Scholar]
  • C.A. Floudas and P.M. Pardalos, A Collection of Test Problems for Constrained Global Optimization Algorithms. Vol. 455. Springer (1990). [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. [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. [Google Scholar]
  • B. Grimstad and B.R. Knudsen, Mathematical programming formulations for piecewise polynomial functions. J. Global Optim. 77 (2020) 455–486. [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. [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. [Google Scholar]
  • D. Henrion and J.B. Lasserre, Solving nonconvex optimization problems. IEEE Control Syst. Mag. 24 (2004) 72–83. [Google Scholar]
  • R. Horst and P.M. Pardalos, Handbook of Global Optimization. Kluwer Academic Publishers, Dordrecht, The Netherlands (1995). [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. [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. [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. [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. [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. [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. [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. [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. [Google Scholar]

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