Characterizations of the Aubin property of the solution mapping for nonlinear semidefinite programming
研究了非线性半定规划在局部最优解处KKT解映射的Aubin性质，证明了强二阶充分条件也是其必要条件，并建立了包括强正则性在内的等价条件。
Abstract In this paper, we study the Aubin property of the Karush-Kuhn-Tucker solution mapping for the nonlinear semidefinite programming (NLSDP) problem at a locally optimal solution. In the literature, it is known that the Aubin property implies the constraint nondegeneracy by Fusek (SIAM J. Optim. 23:1041–1061, 2013) and the second-order sufficient condition by Ding et al. (SIAM J. Optim. 27:67–90, 2017). Based on the Mordukhovich criterion, here we further prove that the strong second-order sufficient condition is also necessary for the Aubin property to hold. Consequently, several equivalent conditions including the strong regularity are established for NLSDP’s Aubin property. Together with the recent progress made by Chen et al. (SIAM J. Optim. 35:712–738, 2025) on the equivalence between the Aubin property and the strong regularity for nonlinear second-order cone programming, this paper constitutes a significant step forward in characterizing the Aubin property for general non-polyhedral $$C^2$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msup> <mml:mi>C</mml:mi> <mml:mn>2</mml:mn> </mml:msup> </mml:math> -cone reducible constrained optimization problems.