We give novel algorithms for stochastic strongly-convex optimization in the gradient oracle model which return a O( 1 T )-approximate solution after T iterations. The first algorithm is deterministic, and achieves this rate via gradient updates and historical averaging. The second algorithm is randomized, and is based on pure gradient steps with a random step size. This rate of convergence is o...

Computing the exact ideal and nadir criterion values is a very ‎important subject in ‎multi-‎objective linear programming (MOLP) ‎problems‎‎. In fact‎, ‎these values define the ideal and nadir points as lower and ‎upper bounds on the nondominated points‎. ‎Whereas determining the ‎ideal point is an easy work‎, ‎because it is equivalent to optimize a ‎convex function (linear function) over a con...

Linear optimization is many times algorithmically simpler than non-linear convex optimization. Linear optimization over matroid polytopes, matching polytopes and path polytopes are example of problems for which we have simple and efficient combinatorial algorithms, but whose non-linear convex counterpart is harder and admit significantly less efficient algorithms. This motivates the computation...

In recent years there has been growing interest in convex optimization techniques for system identification and time series modeling. This interest is motivated by the success of convex methods for sparse optimization and rank minimization in signal processing, statistics, and machine learning, and by the development of new classes of algorithms for large-scale nondifferentiable convex optimiza...

We discuss the approach to estimate aggregation and adaptive estimation based upon (nearly optimal) testing of convex hypotheses. show that in situation where observations stem from simple observation schemes (Juditsky Nemirovski, 2020) set unknown signals is a finite union compact sets, proposed leads adaptation routines with nearly optimal performance. As an illustration, we consider applicat...

ABSTRACT This paper provides a short introduction to the Lagrangian duality in convex optimization. At first the topic is motivated by outlining the importance of convex optimization. After that mathematical optimization classes such as convex, linear and non-convex optimization, are defined. Later the Lagrangian duality is introduced. Weak and strong duality are explained and optimality condit...