The talk will give a broad outline of the recent advances in worst-case evaluation complexity for the nonlinear (possibly nonconvex) optimization problem. Worst-case bounds will be given for the unconstrained, convexly constrained and general constrained problems, and examples will be shown to prove the sharpness of these bounds. Besides the already remarkable fact that such bounds exist, the analysis brings several surprises related to the impact of constraints on complexity and the worst-case performance of well-known algorithms such as Newton's method.
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