Some Modifications of Mirror Prox Algorithm for Strongly Monotone Variational Inequalities and Related Results

The report is devoted to the development of numerical methods for solving variational inequalities with some simplified requirements for the smoothness conditions of functionals. We consider the Mirror Prox algorithm for solving both variational inequalities and saddle point problems. We compare its effectiveness with the recently proposed accelerated method. Further we focus on strongly monotone operators and corresponding variational inequalities. We propose the modification of the Mirror Prox algorithm in the case of relatively strongly monotone operator and compare its effectiveness with the restarted version of the classical Mirror Prox algorithm.