Sufficient Second-Order Optimality Conditions for Semilinear Control Problems with Pointwise State Constraints

Second-order sufficient optimality conditions are established for the optimal control of semilinear elliptic and parabolic equations with pointwise constraints on the control and the state. In contrast to former publications on this subject, the cone of critical directions is the smallest possible in the sense that the second-order sufficient conditions are the closest to the associated necessary ones. The theory is developed for elliptic distributed controls in domains up to dimension three. Moreover, problems of elliptic boundary control and parabolic distributed control are discussed in spatial domains of dimension two and one, respectively. Key words. optimal control, elliptic equations, parabolic equations, pointwise state constraints, second-order necessary optimality conditions, second-order sufficient optimality conditions AMS subject classifications. 49K20,90C48

• Type: Journal
• Year: 2008
• Where: SIAMJO
• Authors: Eduardo Casas, Juan Carlos de los Reyes, Fredi Tröltzsch
• Keywords: Optimality Conditions, Parabolic Equations, Second-order Sufficient Conditions, SIAMJO 2008