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Seminario de Jan J. Rückmann

23 mayo, 2018
12:30 pma1:30 pm

Speaker: Jan J. Rückmann

Title: “Mathematical Programs with Complementarity constraints: Critical Point Theory”

Coauthors: Hubertus Th. Jongen and Vladimir Shikhman.

Date: 23 May.  12:30 h.

Localication: Sala de Seminarios (Edificio Torretamarit)

Abstract. We study mathematical programs with complementarity constraints from a topological point of view. We derive a Morse Lemma at nondegenerate C- stationary points and present two basic theorems from Morse theory (deformation theorem and cell-attachment theorem). Outside the C-stationary point set, continuous deformation of lower level sets can be performed and, as a consequence, the topological data (such as the number of connected components) remain invariant. However, when passing a level containing a C-stationary point, the topology of the lower level set changes via the attachment of a q-dimensional cell where its dimension equals the stationary C-index of the corresponding C- stationary point. The stationary C-index depends on both the restricted Hessian of the Lagrangian and the Lagrange multipliers related to bi-active complementarity constraints. Finally, some relations with other stationarity concepts are discussed.
The lecture is based on a joint paper with Hubertus Th. Jongen and Vladimir Shikhman.

Seminario de Stefan Sperlich

24 mayo, 2018
12:00 pma1:00 pm

Speaker: Stefan Sperlich

Title: Uniform inference for Small Area Parameter

Coauthors: K. Reluga, P. Kramlinger, T. Krivobokova and M.J. Lombardía

Date: 24 May. 12:00 h.

Localication: Sala de Seminarios (Edificio Torretamarit)

Abstract. Today, SAE is a common tool used world-wide by Statistical offices for addressing the need of disaggregated information. Interval estimates can either be extremely wide if not model-based, or only refer to marginal (ie unconditional) distributions. That is, when speaking of a 95% confidence interval, for 5% of the considered areas, the intervals do not contain the true parameter. This is a delicate default if political decisions based on them, and prohibits the comparing areas based on those estimates.  In this work, construction of uniform prediction intervals (or simultaneous confidence sets) for small area parameter in linear mixed models is introduced. We consider three frameworks to develop simultaneous intervals: analytical, numerical and bootstrap approximation. Proofs of the consistency as well as the asymptotic coverage probability of the bootstrap intervals are provided. Our proposal is accompanied by simulation experiments and data examples.

Seminario de Greys Sosic

22 mayo, 2018
12:30 pma2:00 pm

Speaker: Greys Sosic, USC Marshall School of Business, USA

Title: Incentives and Emission Responsibility Allocation in Supply Chains

Date: 22 de May.  12:30 h.

Location: Sala de Seminarios (Edificio Torretamarit)

Abstract: In view of the urgency and challenges of mitigating climate change, it should be noted that Greenhouse Gas (GHG) emitted from the supply chains of the 2,500 largest global corporations accounts for about 18% of global GHG emissions. Therefore, rationalizing emissions in supply chains could make a significant contribution to achieving the CO2 emission reduction targets recently agreed upon in Paris (Paris Agreement, 2015).

In this paper we consider supply chains with  motivated dominant leaders, such as Walmart, who strive to reduce emissions in their supply chains. These supply chain leaders are assumed to be knowledgeable about causes of pollution in their supply chains, to the extent that they are able to assign their suppliers responsibilities for both direct and indirect GHG emissions in the supply chain. Given these pollution responsibility assignments, we use cooperative game theory methodology to derive a scheme for allocating the responsibilities of the total GHG emissions to the firms in the supply chain.

The allocation scheme that we derive, which is the Shapley value of an associated cooperative game, is shown to have several desirable properties. In particular, (i) it is footprint-balanced, (ii) it is transparent and easy to compute, (iii) it lends itself to several intuitive and insightful axiomatic characterizations, and (iv) when the abatement cost functions of the firms are private information, it is shown to incentivize suppliers to exert pollution abatement efforts that, among all footprint-balanced allocation schemes, minimize the maximum deviation from the socially optimal pollution level.