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1 results

  • 4 - Quadratic Functions

  • from Part II - From General Mathematical Background to General Nonlinear Programming Problems (NLP)
  • Vassilios S. Vassiliadis, University of Cambridge, Walter Kähm, Ehecatl Antonio del Rio Chanona, Imperial College London, Ye Yuan
  • Book:
    Optimization for Chemical and Biochemical Engineering
    Published online:
    17 December 2020
    Print publication:
    14 January 2021, pp 44-56

  • Summary

    Quadratic multidimensional functions play a very important role in the understanding of general nonlinear functions. Convexity of quadratic functions is linked in a natural way from its geometrical definition all the way to the properties of its matrix eigenspectrum.Indeed, to second order expansion, and close to the expansion point, any nonlinear function can be approximated by a quadratic – thus providing a crucial link and understanding of the local behaviour and convexity properties of general functions.