An algorithm for optimization problems with functional inequality constraints

Abstract

This paper presents an algorithm for minimizing an objective function subject to conventional inequality constraints as well as to inequality constraints of the functional type: <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">\max_{\omega \in \Omega} \phi(z,\omega) \leq 0</tex> , where Ω is a closed interval in <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">R</tex> , and <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">z \in R^{n}</tex> is the parameter vector to be optimized. The algorithm is motivated by a standard earthquake engineering problem and the problem of designing linear multivariable systems. The stability condition (Nyquist criterion) and disturbance suppression condition for such systems are easily expressed as a functional inequality constraint.