theoretical perspectives and open problems in generalized semi-infinite (multiobjective) nonsmooth optimization

This paper investigates the theoretical aspects of generalized semi-infinite optimization problems (gsip) in both single- and multiobjective nonsmooth settings. a concise overview of existing results on optimality conditions, subdifferential analysis, and constraint qualifications is presented. the discussion highlights unresolved theoretical issues, including extensions of karush–kuhn–tucker-type conditions, stability analysis, duality, and characterization of effcient solutions under nonsmoothness. finally, several open problems are identified to motivate further research in (multiobjective) gsip.