Well-posedness without semicontinuity for parametric quasiequilibria and quasioptimization

We consider quasiequilibrium and quasioptimization problems. A relaxed level closedness notion is proposed and used together with pseudocontinuity to establish sufficient conditions for parametric well-posedness and well-posedness without semicontinuity assumptions. We prove them in general formulations, though such relaxations allow us to improve some existing results even in simple cases of R1R1. Several new well-posedness results are also obtained. For topological settings we use sensitivity analysis while for problems on metric spaces we argue on diameters and Kuratowski’s and Hausdorff’s measures of noncompactness of approximate solution sets.