This talk presents an overview of research results on calmness of linear optimization problems. Calmness of the feasible set and the optimal set mappings is studied in the setting of canonical perturbations, and also in the framework of full perturbations. While there exists a clear proportionality between the calmness moduli of the feasible set mappings in both contexts, the analysis of the relationship between the calmness moduli of the argmin mappings is much more complicated. Point-based expressions (only involving the nominal problem's data) for the calmness moduli are provided. Some applications are commented, specifically one related to measures of the convergence of interior point methods.
Marco A. López-Cerdá received his Doctor Degree from Valencia University in 1973. In 1981 he became Full Professor at Valencia University; in 1985 moved to Alicante University. He is Doctor Honoris Causa by the University of Limoges (July, 2012), and Corresponding Member of the Spanish Real Academy of Sciences. (Co)adviser of 17 Ph.D. students in several branches of Operations Research such as semi-infinite programming, convex optimization, game theory and variational analysis. He has been Chief Investigator in several projects, both theoretical (basic research) and applied (for the university community services, the city and the province of Alicante, and banking industry).
His 1998 book (with M.A. Goberna) on Linear Semi-Infinite Optimization has become a classical in the field. 139 publications, 1379 citations by 482 authors (according to MathSciNet) in first-rank journals as Math. Programming, MOR, SIOPT, JOTA, Optimization, etc.
Other positions are: Co-editor in Chief of TOP (the OR journal of SEIO, the Spanish Society of Statistics and Operations Research) from 2000 to 2007, elected president of SEIO in 1986, chair of EUROPT in the period 2008-2010, coordinator of i-MATH Consolider (2006-2011), a huge project of the Spanish Ministry of Education for all areas of mathematics, gathering more than 300 research groups, and with a budget of 7.5 million euros.