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Second-Order Sufficient Conditions for Weak Local Minima: General Control Constraints

In: New Trends and Challenges in Optimization Theory Applied to Space Engineering

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  • Helene Frankowska

    (Sorbonne Université)

Abstract

We present second-order sufficient optimality conditions for the Mayer optimal control problem under general control constraints. For this aim we assume that neighboring controls can be approximated by second-order tangents relative to critical directions. This is always the case when the control constraints are described by functional inequalities involving C 2 $$C^2$$ functions with linearly independent gradients of active constraints. Sufficient conditions are expressed then by strengthening the known inequalities of the second-order necessary conditions.

Suggested Citation

  • Helene Frankowska, 2025. "Second-Order Sufficient Conditions for Weak Local Minima: General Control Constraints," Springer Optimization and Its Applications, in: Piermarco Cannarsa & Alessandra Celletti & Giorgio Fasano & Leonardo Mazzini & Mauro Pontani & Emman (ed.), New Trends and Challenges in Optimization Theory Applied to Space Engineering, pages 185-194, Springer.
    • Handle: RePEc:spr:spochp:978-3-031-81253-8_13
    DOI: 10.1007/978-3-031-81253-8_13
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