Duality for a class of multiobjective control problems. (Q5961173)

In this paper a class of multiobjective control problems is considered, where the objective and constraint functions involved are \(f(t,x(t),x'(t),y(t),z(t))\) with \(x(t),y(t)\in {\mathbb R}^n,\) and \(z(t)\in {\mathbb R}^m,\) \(x(t)\) and \(z(t)\) are the control variables and \(y(t)\) is the state variable. The Wolfe--type and the Mond--Wier--type vector control dual problems for properly efficient solutions are considered. Under invexity assumptions, weak, strong and converse duality results are proved through a parametric approach.