Simultaneous optimization and solution of systems described by differential/algebraic equations

Abstract

Engineering approaches to the solution of constrained variational problems often involve converting the problem into a nonlinear programming (NLP) problem and solving it using current NLP methods. These methods usually use a sequential optimization and solution strategy. We propose a method, using piecewise constant functions for the independent variables, that combines the technologies of quasi-Newton optimization algorithms and global spline collocation to simultaneously optimize and integrate systems described by differential/algebraic equations. A computer implementable algorithm is discussed and three test problems are solved. The algorithm allows the solution of a more general class of optimization problems than previous methods employing this strategy.