Scientific contributions of Leo Khachiyan (a short overview)

On April 29, 2005, Leo Khachiyan passed away with tragic suddenness in the middle of his scientific career. He became famous for his polynomial time algorithm for linear programming (LP)[L. Khachiyan, A polynomial algorithm in linear programming, Soviet Math. Doklady 20 (1) (1979) 191-194; L. Khachiyan, Polynomial algorithms for linear programming, USSR Comp. Math. and Math. Phys. 20 (2) (1980) 51-68]. However, he contributed fundamentally to several other areas, as well. In this introductory paper, we would like to recall briefly his main contributions, and provide a complete (up to our best knowledge) list of his publications.