On optimality conditions and duality theorems for robust semi-infinite multiobjective optimization problems
The authors consider a robust version to the following uncertain semi-infinite multibojective optimization problem: \[ \min (f_1(x), \dots f_k(x))\text{ subject to }g_t(x, \nu_t) \leq 0,~ t \in T,\tag{1} \] where \(f_i: \mathbb R^n \rightarrow \mathbb R\), \(i = 1, \dots, k\), \(g_t: \mathbb R^n \times \mathbb R^q \rightarrow \mathbb R\) are continuously differentiable, \(\nu_t \in \mathbb R^q\) are uncertain parameters belonging to a convex compact set and \(T\) is an arbitrary possibly infinite index set. Let \(R\) denote the set of feasible solutions of Problem (1). An element \(\tilde{x} \in R\) is called a weakly robust efficient solution of Problem (1) if it does not exist another solution \(x\in R\) such that \(f_i(x) < f_i(\tilde{x})\), \(1 \leq i \leq k \). Necessary and sufficient optimality conditions of weakly robust efficiency are proved. Corresponding duality theory is developed. As a special case, linear semi-infnite robust optimization problems are investigated.
scientific article; zbMATH DE number 7032541
scientific article