WIAS Preprint No. 2762, (2020)

State-constrained control-affine parabolic problems I: First and second order necessary optimality conditions


  • Aronna, M. Soledad
    ORCID: 0000-0002-0640-4722
  • Bonnans, J. Frédéric
  • Kröner, Axel

2010 Mathematics Subject Classification

  • 49J20 49K20 35J10 93C20


  • Optimal control of partial differential equations, semilinear parabolic equations, state constraints, second order analysis, control-affine problems




In this paper we consider an optimal control problem governed by a semilinear heat equation with bilinear control-state terms and subject to control and state constraints. The state constraints are of integral type, the integral being with respect to the space variable. The control is multidimensional. The cost functional is of a tracking type and contains a linear term in the control variables. We derive second order necessary conditions relying on the concept of alternative costates and quasi-radial critical directions.

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