At the beginning of this talk, we review condition numbers for linear systems and linear conic systems. Later, we review the notion of condition for set-valued mappings and equations introduced by Dontchev and Rockafellar.
In the main part of the talk, we present an application of that approach to study the condition number of two-stage stochastic programs. More precisely, we consider linear-quadratic stochastic programs with discrete probability measures. The latter is based on joint work with K. Emich and R. Henrion.
Professor Rӧmisch is the most recent recipient of the Khachiyan Prize of INFORMS Optimization Society. He is a professor emeritus from Humboldt University in Berlin, Germany. Rӧmisch is one of the main contributors to stochastic optimization under uncertainty and risk. He has developed the only universally applicable methodology for scenario tree generation, novel models of risk termed “polyhedral measures of risk,” and has introduced quasi Monte Carlo methods to stochastic optimization. He is the most recognized expert in the area of stability and sensitivity analysis of stochastic optimization models.
Rӧmisch has led work on many complex applied problems within the areas of power generation and distribution, power networks, gas transportation networks, airline revenue management and in the chemical industry. He has substantial contributions to education in form of textbooks, lecture notes, contributions to handbooks and encyclopedias. He has been serving on the editorial boards of the SIAM Journal on Optimization, Computational Management Science, Energy Systems, and Optimization Letters.