LINDO Global employs branch-and-cut methods to break an nonlinearly constrained optimization problem model down into a list of subproblems. Each subproblem is analyzed and either a) is shown to not have a feasible or optimal solution, or b) an optimal solution to the subproblem is found, e.g., because the subproblem is shown to be convex, or c) the subproblem is further split into two or more subproblems which are then placed on the list. Given appropriate tolerances, after a finite, though possibly large number of steps a solution provably global optimal to tolerances is returned.

References in zbMATH (referenced in 30 articles , 1 standard article )

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  1. Andrea Callia D’Iddio, Michael Huth: Manyopt: An Extensible Tool for Mixed, Non-Linear Optimization Through SMT Solving (2017) arXiv
  2. Khan, Kamil A.; Watson, Harry A.J.; Barton, Paul I.: Differentiable McCormick relaxations (2017)
  3. Newby, Eric; Ali, M.M.: Linear transformation based solution methods for non-convex mixed integer quadratic programs (2017)
  4. Puranik, Yash; Sahinidis, Nikolaos V.: Bounds tightening based on optimality conditions for nonconvex box-constrained optimization (2017)
  5. Birgin, E.G.; Lobato, R.D.; Martínez, J.M.: Packing ellipsoids by nonlinear optimization (2016)
  6. Boukouvala, Fani; Misener, Ruth; Floudas, Christodoulos A.: Global optimization advances in mixed-integer nonlinear programming, MINLP, and constrained derivative-free optimization, CDFO (2016)
  7. Grimstad, Bjarne; Sandnes, Anders: Global optimization with spline constraints: a new branch-and-bound method based on B-splines (2016)
  8. Zhang, Yan; Sahinidis, Nikolaos V.: Global optimization of mathematical programs with complementarity constraints and application to clean energy deployment (2016)
  9. Bao, Xiaowei; Khajavirad, Aida; Sahinidis, Nikolaos V.; Tawarmalani, Mohit: Global optimization of nonconvex problems with multilinear intermediates (2015)
  10. Frank, Stephen M.; Rebennack, Steffen: Optimal design of mixed AC-DC distribution systems for commercial buildings: a nonconvex generalized Benders decomposition approach (2015)
  11. Berthold, Timo: RENS. The optimal rounding (2014)
  12. Berthold, Timo; Gleixner, Ambros M.: Undercover: a primal MINLP heuristic exploring a largest sub-MIP (2014)
  13. Khazaei, Javad; Downward, Anthony; Zakeri, Golbon: Modelling counter-intuitive effects on cost and air pollution from intermittent generation (2014)
  14. Misener, Ruth; Floudas, Christodoulos A.: ANTIGONE: algorithms for coNTinuous/Integer global optimization of nonlinear equations (2014)
  15. Misener, Ruth; Floudas, Christodoulos A.: A framework for globally optimizing mixed-integer signomial programs (2014)
  16. Newby, Eric; Ali, M.M.: A note on convex reformulation schemes for mixed integer quadratic programs (2014)
  17. Zorn, Keith; Sahinidis, Nikolaos V.: Global optimization of general nonconvex problems with intermediate polynomial substructures (2014)
  18. Zorn, Keith; Sahinidis, Nikolaos V.: Global optimization of general non-convex problems with intermediate bilinear substructures (2014)
  19. Belotti, Pietro: Bound reduction using pairs of linear inequalities (2013)
  20. Janes, Pete P.; Rendell, Alistair P.: Deterministic global optimization in ab-initio quantum chemistry (2013)

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