Upcoming events:

### Rates of convergence for the Krasnoselskii-Mann fixed point iteration (ISOR)

by Roberto Cominetti (Univ. A. Ibanez, Santiago de Chile)

Date:           23th April 2018 - Time: 16:45-17:45

Location:      HS 7 (lecture room)
Uni Vienna
(Oskar-Morgenstern-Platz 1, 1090 Vienna)

Abstract:

We analyze the convergence of an inexact version of the classical Krasnoselskii-Mann iteration for computing fixed points of nonexpansive maps in Banach spaces. Our main result establishes a new metric bound for the fixed-point residuals, from which we derive their rate of convergence as well as the convergence of the iterates towards a fixed point. To this end we consider a nested family of optimal transport problems that provide a recursive bound for the distance between the iterates. These recursive bounds are in turn interpreted as expected rewards for an underlying Markov chain, which leads to explicit rates of convergence. In the case of the exact iteration we show that these bounds are tight by building a nonexpansive map that attains them with equality, and we deduce that the optimal constant of asymptotic regularity is exactly $1/\sqrt{\pi}$. The results are extended to continuous time to study the asymptotics of non-autonomous evolution equations governed by nonexpansive operators.

### Sensitivity Analysis for Convex Separable Optimization over Integral Polymatroids (ISOR)

by Tobias Harks(Univ. Augsburg)

Date:           7th Mai2018 - Time: 16:45-17:45

Location:      HS 7 (lecture room)
Uni Vienna
(Oskar-Morgenstern-Platz 1, 1090 Vienna)

Abstract:

The talk will discuss the sensitivity of optimal solutions of convex separable optimization problems over an integral polymatroid base polytope with respect to parameters determining both the cost of each element and the polytope. Under convexity and a regularity assumption on the functional dependency of the cost function with respect to the parameters, it is shown show that reoptimization after a change in parameters can be done by elementary local operations. I will show that these sensitivity results can be applied to a new class of non-cooperative games played on integral polymatroid base polytopes in order to compute pure Nash equilibria.

### First order algorithms for constrained optimization problems in Machine Learning (ISOR)

Date:           14th Mai2018 - Time: 16:45-17:45

Location:      HS 7 (lecture room)
Uni Vienna
(Oskar-Morgenstern-Platz 1, 1090 Vienna)

Abstract:

Thanks to the advent of the "Big Data era", simple iterative first-order optimization approaches for constrained convex optimization have re-gained popularity in the last few years. In the talk, we first review a few classic methods (i.e., conditional and projected gradient method) in the context of Big Data applications. Then, we discuss both theoretical and computational aspects of some new active-set variants for those classic methods. Finally, we examine current challenges and future research perspectives.

### Robust Nonlinear Optimization with Convex Uncertainty

by Dick den Hertog(Univ. Tilburg)

Date:           18th June 2018 - Time: 16:45-17:45

Location:      HS 7 (lecture room)
Uni Vienna
(Oskar-Morgenstern-Platz 1, 1090 Vienna)

Abstract:

Robust Optimization is a popular approach to treat uncertainty in optimization problems. Finding a computationally tractable formulation of the robust counterpart of an optimization problem is key in being able to apply this approach. In the first part of the presentation we will give an introduction to Robust Optimization. Although techniques for finding a robust counterpart are available for many types of constraints, no general techniques exist for functions that are convex in the uncertain parameter. Such constraints are, however, common in, e.g., quadratic optimization and geometric programming problems. In the second part of this presentation, we provide a systematic way to construct a safe approximation to the robust counterpart of a nonlinear uncertain inequality that is convex in the uncertain parameters for a polyhedral uncertainty set. We use duality theory as well as adjustable robust optimization techniques to obtain this approximation. We also propose a general purpose method to strengthen the obtained approximation by using nonlinear decision rules for the introduced auxiliary adjustable variables. We show the quality of the approximations by performing several numerical experiments.

### The Nutritious Supply Chain: Optimizing Humanitarian Food Aid (VCOR)

by Dick den Hertog(Univ. Tilburg)

Date:           18th June 2018 - Time: tba (approximately between 13:00 and 15:00)

Location:      tba
Uni Vienna
(Oskar-Morgenstern-Platz 1, 1090 Vienna)

Abstract:

The UN World Food Programme (WFP) is the largest humanitarian agency fighting hunger worldwide, reaching around 80 million people with food assistance in 75 countries each year. To deal with the operational complexities inherent to its mandate, WFP has been developing tools to assist their decision makers with integrating the supply chain decisions across departments and functional areas. This presentation describes a mixed integer linear programming model that simultaneously optimizes the food basket to be delivered, the sourcing plan, the routing plan, and the transfer modality of a long-term recovery operation for each month in a pre-defined time horizon. By connecting traditional supply chain elements to nutritional objectives, we made significant breakthroughs in the operational excellence of WFP’s most complex operations, such as Iraq and Yemen. We show how we used optimization to reduce the operational costs in Iraq by 17%, while still supplying 98% of the nutritional targets. Additionally, we show how we are using optimization in Yemen to manage the scale-up of the existing operation from three to six million beneficiaries.

Co-authors: Koen Peters, Hein Fleuren, Mirjana Kavelj, Sérgio Silva, Rui Gonçalves, Ozlem Ergun, Mallory Soldner