Algorithms for Special Nonlinear Programming Problems

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This project focuses on the use of nonsmooth penalty functions in nonlinear programming methods, in particular in the areas of semi-infinite programming, complex linear approximation in the nor l-one and constrained optimal control. Penalty functions usually have complicated structure, or else are nonsmooth, making it necessary to devise special techniques for their minimization. The investigator plans to extend and apply known algorithms to some new areas of nonlinear programming. Four areas will be investigated from this point of view: complex l-one approximations, inexactness of the second-order correction method, semi-infinite programming and discretized optimal control problems. Algorithmic questions will be addressed, and numerical experiments will be performed on a supercomputer. This research falls into the general area of nonlinear programming and computational optimization which has numerous applications in engineering and management science.