Invited Session Fri.2.MA 313

Friday, 13:15 - 14:45 h, Room: MA 313

Cluster 3: Complementarity & variational inequalities [...]

Variational inequality problems: Analysis and computation

 

Chair: Vinayak Shanbhag

 

 

Friday, 13:15 - 13:40 h, Room: MA 313, Talk 1

Huifu Xu
Quantitative stability analysis of stochastic generalized equations and applications

Coauthors: Yongchao Liu, Werner Römisch

 

Abstract:
We consider a stochastic generalized equation (SGE)
where the underlying function is the expected value of a random set-valued mapping. SGE has many applications such as
characterizing optimality conditions of a nonsmooth stochastic optimization problem and a stochastic equilibrium problem. We derive quantitative continuity of expected value of the set-valued mapping with respect to the variation of the underlying probability measure in a metric space. This leads to the subsequent qualitative and quantitative
stability analysis of solution set mappings of the SGE. Under some metric regularity conditions, we derive
Aubin's property of the solution set mapping with respect to
the change of probability measure. The established results are applied to stability analysis of stationary points of classical one stage and two stage stochastic minimization
problems, two stage stochastic mathematical programs with equilibrium constraints and stochastic programs with second order dominance constraints.

 

 

Friday, 13:45 - 14:10 h, Room: MA 313, Talk 2

Che-Lin Su
Estimation of pure characteristics demand models with pricing

Coauthors: Yu-Ching Lee, Jong-Shi Pang

 

Abstract:
A pure characteristics model is a class of discrete-choice random-coefficients demand models in which there is no idiosyncratic logit error term in a consumer's utility.
The absence of the logit error term leads to a nonsmooth formulation of the predicted market share equations. As a result, inverting the market share equations for the unobserved
product characteristics and estimating the model by using the nested fixed-point approach as proposed in the existing econometrics literature becomes computationally intractable.
We introduce lotteries for consumers' purchase decisions, which are then characterized by a system of complementarity constraints. This reformulation leads to smooth market share
equations. Based on this reformulation, we then cast the generalized method of moments (GMM) estimation of a pure characteristics model as a quadratic program with
nonlinear complementarity constraints. We present numerical results to demonstrate the effectiveness of our approach.

 

 

Friday, 14:15 - 14:40 h, Room: MA 313, Talk 3

Vinayak Shanbhag
On the analysis and solution of stochastic variational inequalities

Coauthor: Uma Ravat

 

Abstract:
We consider the stochastic variational inequality problem in which the mappings contain expectations over a possibly general measure space and associated sets may be unbounded. In this talk, we consider two fundamental questions. First, we provide tractable verifiable conditions for showing existence that do not necessitate integration. Important such conditions are provided for quasi-variational inequalities and complementarity problems and can further accommodate multivalued maps and nonconvex sets. Second, we discuss some stochastic approximation schemes for monotone stochastic variational inequalities that incorporate regularization and allow for adaptive modifications of steplengths.

 

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