LAUSR

We aim to establish Karush-Kuhn-Tucker multiplier rules involving higher-order complementarity slackness under Holder metric subregularity. These rules may be in the nonclassical form, i.e., their right-hand side is a supremum expression (instead of zero as in the classical form). We consider a general problem setting of set-valued optimization and are interested in some typical types of solutions: weak, Henig-proper, positively-proper, and Borwein-proper solutions. To this end, we propose and apply a concept of a quasi-contingent derivative of index $\gamma \in [0,\infty ]$ and define suitable critical directions. We impose generalized constraint qualifications of the Mangasarian-Fromovitz and Kurcyusz-Robinson-Zowe types to have nonvanishing objective multipliers. Our results are new or improve significantly recent existing ones.