By Y. Nesterov
It was once in the course of the Eighties, while the seminal paper by means of Kar markar opened a brand new epoch in nonlinear optimization. the significance of this paper, containing a brand new polynomial-time set of rules for linear op timization difficulties, used to be not just in its complexity certain. at the moment, the main unbelievable function of this set of rules was once that the theoretical pre diction of its excessive potency was once supported via very good computational effects. This strange truth dramatically replaced the fashion and direc tions of the examine in nonlinear optimization. Thereafter it turned a growing number of universal that the recent tools have been supplied with a complexity research, which used to be thought of a greater justification in their potency than computational experiments. In a brand new swiftly boost ing box, which bought the identify "polynomial-time interior-point methods", this type of justification was once compulsory. Afteralmost fifteen years of extensive examine, the most result of this improvement began appearing in monographs [12, 14, sixteen, 17, 18, 19]. nearly at the moment the writer was once requested to arrange a brand new path on nonlinear optimization for graduate scholars. the belief was once to create a direction which might mirror the recent advancements within the box. truly, this used to be an incredible problem. on the time in basic terms the speculation of interior-point equipment for linear optimization was once polished adequate to be defined to scholars. the final thought of self-concordant capabilities had seemed in print just once within the kind of learn monograph .