非一致凸积分的二阶条件:$L^1$的二次增长

Journal of Nonsmooth Analysis and Optimization Pub Date : 2021-11-19 DOI:10.46298/jnsao-2022-8733

D. Wachsmuth, G. Wachsmuth

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引用次数: 7

摘要

研究了一类非均匀凸非光滑积分泛函的无间隙二阶最优性条件。将积分泛函推广到测度空间。得到的二阶导数包含了低维流形上的积分。证明利用了凸预共轭，它是连续函数空间上的一个积分泛函。给出了非光滑最优控制问题的应用。

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Second-order conditions for non-uniformly convex integrands: quadratic growth in $L^1$

We study no-gap second-order optimality conditions for a non-uniformly convex and non-smooth integral functional. The integral functional is extended to the space of measures. The obtained second-order derivatives contain integrals on lower-dimensional manifolds. The proofs utilize the convex pre-conjugate, which is an integral functional on the space of continuous functions. Applications to non-smooth optimal control problems are given.

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Journal of Nonsmooth Analysis and Optimization

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