Model Building and Practical Aspects of Nonlinear Programming

Many optimization problems arise from complex models of real-world phenomena. This paper examines the close relationship between certain features of well-posed models and robust optimization methods. First, a list of modelling principles is given, to aid in formulating models suited to solution by modern optimization methods. Quasi-Newton sequential quadratic programming methods for nonlinearly constrained optimization are then discussed. The topics considered include representation and definition of the approximate Hessian of the Lagrangian function; similarities between primal and dual quadratic programming methods; treatment of inconsistent and ill-conditioned subproblems; and properties of various active-set strategies. Finally, the results of solving several test problems are analyzed in detail, including significant characteristics of the overall solution process such as superlinear convergence. Keywords: Sequential quadratic programming; Quasi-Newton methods; Numerical methods; Optimization. (Author).