MC++

MC++ is a library that computes convex/concave bounds and Taylor models for enclosing the range of factorable functions. Factorable functions are those defined as a finite recursive composition of binary sums, binary products and univariate functions; this is an extremely inclusive class of functions containing nearly every function which can be represented finitely on a computer. The main applications of MC++ are in the area of deterministic global optimization as well as for the verified solution of nonlinear algebraic equations and ordinary differential equations (ODEs). MC++ is programmed in C++ and makes extensive use of class templates and operator overloading. Although less performant than source code tranformation, this approach offers great flexibility and is particularly well suited for proof-of-concept implementations. Moreover, it is perfectly adequate for many small- to medium-size problems. MC++ is the successor of libMC.


References in zbMATH (referenced in 12 articles )

Showing results 1 to 12 of 12.
Sorted by year (citations)

  1. Chen, Qi; Johnson, Emma S.; Bernal, David E.; Valentin, Romeo; Kale, Sunjeev; Bates, Johnny; Siirola, John D.; Grossmann, Ignacio E.: Pyomo.GDP: an ecosystem for logic based modeling and optimization development (2022)
  2. Huster, Wolfgang R.; Schweidtmann, Artur M.; Mitsos, Alexander: Working fluid selection for organic rankine cycles via deterministic global optimization of design and operation (2020)
  3. Najman, Jaromił; Mitsos, Alexander: On tightness and anchoring of McCormick and other relaxations (2019)
  4. Schweidtmann, Artur M.; Mitsos, Alexander: Deterministic global optimization with artificial neural networks embedded (2019)
  5. Bongartz, Dominik; Mitsos, Alexander: Deterministic global optimization of process flowsheets in a reduced space using McCormick relaxations (2017)
  6. Harwood, Stuart M.; Barton, Paul I.: How to solve a design centering problem (2017)
  7. Khan, Kamil A.; Watson, Harry A. J.; Barton, Paul I.: Differentiable McCormick relaxations (2017)
  8. Stuber, Matthew D.; Scott, Joseph K.; Barton, Paul I.: Convex and concave relaxations of implicit functions (2015)
  9. Wechsung, Achim; Scott, Joseph K.; Watson, Harry A. J.; Barton, Paul I.: Reverse propagation of McCormick relaxations (2015)
  10. Tsoukalas, A.; Mitsos, A.: Multivariate McCormick relaxations (2014)
  11. Bompadre, Agustín; Mitsos, Alexander; Chachuat, Benoît: Convergence analysis of Taylor models and McCormick-Taylor models (2013)
  12. Bompadre, Agustín; Mitsos, Alexander: Convergence rate of McCormick relaxations (2012)