Making hard constraints soft

ABSTRACT

Search algorithms solve a problem by evaluating a user defined function at a sequence of points that tend to converge to the desired solution. If the function contains an expression such as (cos x - e^y sin z)^1/2 which can not be evaluated at some points, the search algorithm may fail at some intermediate point. Faced with such a problem one is inclined to think of using an algorithm that allows one to impose constraints. (For this example, cos x - e^y sin z ≥ 0.) But unlike most constraints that are imposed, we need to impose the condition that no attempt be made to evaluate the function (or perhaps another constraint) when the constraint is not satisfied. I call such a constraint a "hard" constraint.²

INDEX TERMS

Classification:
  G. Mathematics of Computing
  G.1 NUMERICAL ANALYSIS
      G.1.6 Optimization
          Subjects: Constrained optimization

General Terms:
Algorithms, Theory