Multiplier - Continuation Algorithms for Constrained Optimization

Several path following algorithms based on the combination of three smooth penalty functions, the quadratic penalty for equality constraints and the quadratic loss and log barrier for inequality constraints, their modern counterparts, augmented Lagrangian or multiplier methods, sequential quadratic programming, and predictorcorrector continuation are described. In the first phase of this methodology, one minimizes the unconstrained or linearly constrained penalty function or augmented A homotopy path generated from the functions is then followed to steps are asymptotic to those taken b sequential quadratic programming which can robust, and a competitive alternative to sequential quadratic programming. optima Lagranf ity a using efficient predictor-corrector continuation methods. The continuation Numerica i test results show the method to be efficient, be used in the final steps. *The work of the first author was partially supported by the National Aeronautics and Space Administration through NASA Grant # NGT-06-002-802. **The second and third authors were supported in part by the Air Force Office of Scientific Research through Grant # AFOSR-884059.