An algorithm for computing Kuhn-Tucker curves of one-parametric semi-infinite optimization problems p(t), t∈&λτ;∼ is presented. Starting with a Kuhn-Tucker point x for a fixed t an underdetermined system of nonlinear equations is used to describe a piece of the Kuhn-Tucker curve (t(α),x(α)) by continuation methods. An active-set-strategy is applied to obtain a new system defining another part of that curve. In addition, a formula for one-sided derivatives of the value-function of p(t) is derived. Numerical examples from air-pollution control and Chebyshev approximation by splines with free knots are presented.
