On optimality conditions and duality theorems for robust semi-infinite multiobjective optimization problems

In this paper, we consider a semi-infinite multiobjective optimization problem with more than two differentiable objective functions and uncertain constraint functions, which is called a robust semi-infinite multiobjective optimization problem and give its robust counterpart $${\mathrm{(RSIMP)}}$$(RSIMP) of the problem, which is regarded as the worst case of the uncertain semi-infinite multiobjective optimization problem. We prove a necessary optimality theorem for a weakly robust efficient solution of $${\mathrm{(RSIMP)}} $$(RSIMP), and then give a sufficient optimality theorem for a weakly robust efficient solution of $${\mathrm{(RSIMP)}}$$(RSIMP). We formulate a Wolfe type dual problem of $${\mathrm{(RSIMP)}}$$(RSIMP) and give duality results which hold between $${\mathrm{(RSIMP)}}$$(RSIMP) and its dual problem.