Solution of general nonlinear optimization problems using the penalty/modified barrier method with the use of exact Hessians

This paper presents the application of the penalty/modified barrier function (PE/MBF) method for the solution of general nonlinear optimization problems. Equality constraints are dealt with by including them directly in the inner optimization problem of the PE/MBF method, and then using their derived symbolic/exact Hessian and gradient information throughout. The PE/MBF, as implemented, consists of a two-stage approach: an outer cycle where the Lagrange multipliers for simple bound constraints of the variables are updated and an inner cycle, where the resulting equality-only constrained nonlinear optimization problem is solved. At present, inequalities in the problem are converted to equalities with the addition of slack variables, and subsequently solved as such, with bounds applied on the slack variables. The advantages of the PE/MBF method are demonstrated with test cases coming from the standard literature of process systems engineering, which also involve optimal control problems.

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