Constraint-Related Reinterpretation of Fundamental Physical Equations Can Serve as a Built-In Regularization

  • Vladik KreinovichEmail author
  • Juan Ferret
  • Martine Ceberio
Part of the Studies in Computational Intelligence book series (SCI, volume 539)


Many traditional physical problems are known to be ill-defined: a tiny change in the initial condition can lead to drastic changes in the resulting solutions. To solve this problem, practitioners regularize these problem, i.e., impose explicit constraints on possible solutions (e.g., constraints on the squares of gradients). Applying the Lagrange multiplier techniques to the corresponding constrained optimization problems is equivalent to adding terms proportional to squares of gradients to the corresponding optimized functionals. It turns out that many optimized functionals of fundamental physics already have such squares-of-gradients terms. We therefore propose to re-interpret these equations – by claiming that they come not, as it is usually assumed, from unconstrained optimization, but rather from a constrained optimization, with squares-of-gradients constrains. With this re-interpretation, the physical equations remain the same – but now we have a built-in regularization; we do not need to worry about ill-defined solutions anymore.


constraints fundamental physics regularization ill-defined problems 


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Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • Vladik Kreinovich
    • 1
    Email author
  • Juan Ferret
    • 2
  • Martine Ceberio
    • 1
  1. 1.Department of Computer ScienceUniversity of Texas at El PasoEl PasoUSA
  2. 2.Department of PhilosophyUniversity of Texas at El PasoEl PasoUSA

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