The purpose of this book is to provide a unified, insightful, and original treatment of robust and adaptive optimization.
Part I describes linear RO and the underlying uncertainty sets.
Part II treats modeling, exact and approximate algorithms for ARO.
Part III introduces nonlinear RO for concave uncertainty.
Part IV outlines nonlinear RO for convex uncertainty.
Part V discusses the theory of distributionally RO and ARO.
Part VI contains a variety of RO and ARO applications including queueing theory, auction design, option pricing and energy unit commitment.
There are some distinguishing characteristics in our selection of the particular structure of the book we would like to comment on:
Our unifying treatment of RO and ARO. We present RO and ARO for LO in Parts I and II, and we return to RO for nonlinear optimization in Parts III and IV, as opposed to presenting RO first and then ARO. The reason is that ARO offers new and very effective ways to solve RO problems, a fact not fully recognized earlier.
Our treatment of nonlinear RO in Parts III and IV using concave and convex uncertainty respectively, as opposed to treating robust conic optimization.
Our extensive treatment of a variety of applications of RO and ARO in several fields in Part VI is guided by the quote of George Dantzig at the beginning of the preface.
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