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The second half of the book describes fully important algorithms in current use such as variable metric methods for unconstrained problems and penalty function methods for constrained problems.

Duality theory - the various nonlinear generaliz ations of the well-known duality theorem of linear program ming - is found relevant also to optimal control, and the , PREFACE Pontryagin theory for optimal control also illuminates finite dimensional problems.

This book contains a rigorous coverage of those topics (and only those topics) that, in the author's judgement, are suitable for inclusion in a first course on Complex Functions.

Many of the results of Chapter 9 do indeed generalize to higher dimensions (and the general machinery of simplicial homology theory is avai1able from earlier chapters) but I have confined myself to one example, namely the theorem that non-orientable closed surfaces do not embed in three-dimensional space.