Set optimization - a rather short introduction

Recent developments in set optimization are surveyed and extended including various set relations as well as fundamental constructions of a convex analysis for set- and vector-valued functions, and duality for set optimization problems. Extensive sections with bibliographical comments summarize the state of the art. Applications to vector optimization and financial risk measures are discussed along with algorithmic approaches to set optimization problems

Measurement of the inclusive and fiducial tt ¯ production cross-sections in the lepton+jets channel in pp collisions at s √ =8 TeV with the ATLAS detector

The inclusive and fiducial tt ¯ production cross-sections are measured in the lepton+jets channel using 20.2 fb −1 of proton-proton collision data at a centre-of-mass energy of 8 TeV recorded with the ATLAS detector at the LHC. Major systematic uncertainties due to the modelling of the jet energy scale and b -tagging efficiency are constrained by separating selected events into three disjoint regions. In order to reduce systematic uncertainties in the most important background, the W+jets process is modelled using Z+jets events in a data-driven approach. The inclusive tt ¯ cross-section is measured with a precision of 5.7% to be σ inc (tt ¯ ) = 248.3 ± 0.7 (stat.) ± 13.4 (syst.) ± 4.7 (lumi.) pb, assuming a top-quark mass of 172.5 GeV. The result is in agreement with the Standard Model prediction. The cross-section is also measured in a phase space close to that of the selected data. The fiducial cross-section is σ fid (tt ¯ ) = 48.8 ± 0.1 (stat.) ± 2.0 (syst.) ± 0.9 (lumi.) pb with a precision of 4.5%

Affinity and Well-Posedness for Optimal Control Problems in Hilbert Spaces

Quadratic optimal control problems in Hilbert spaces are considered. We show that well-posedness of problems without constraints for all desired trajectories is equivalent to affinity on the control of the dynamics in the abstract Cauchy problem