We introduce the general and powerful scheme of predicting information re-use in optimization algorithms. This allows us to devise a computationally efficient algorithm for bandit convex optimization with new state-of-the-art guarantees for both Lipschitz loss functions and loss functions with Lipschitz gradients. This is the first algorithm admitting both a polynomial time complexity and a reg...

We introduce the convex combinatorial optimization problem, a far-reaching generalization of the standard linear combinatorial optimization problem. We show that it is strongly polynomial time solvable over any edge-guaranteed family, and discuss several applications.

A SUMMARY BY DIMITRI P. BERTSEKAS We provide a summary of theoretical concepts and results relating to convex analysis, convex optimization, and duality theory. In particular, we list the relevant definitions and propositions (without proofs) of the author’s book “Convex Optimization Theory,” Athena Scientific, 2009. For ease of use, the chapter, section, definition, and proposition numbers of ...

Robust nonlinear optimization is not as well developed as the linear case, and limited in the constraints and uncertainty sets it can handle. In this work we extend the scope of robust optimization by showing how to solve a large class of robust nonlinear optimization problems. The fascinating and appealing property of our approach is that any convex uncertainty set can be used. We give an expl...