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<p>We take into consideration the classical saddle point conditions for programming problems involving convex functions, linear affine functions and a convex set constraint. We prove a nonlinear theorem of the alternative, and we discuss the relationships between the Slater constraint qualification and a constraint qualification proposed by Neustadt (Neustadt LW. Academic Press, New York, pp 323–348,1970) .</p>

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A note on constraint qualification for saddle point conditions involving convex and linear affine functions

  • 期刊论文

  • 发表日期：

    2026年5月4日

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  • G. Giorgi,
  • B. Jiménez,
  • V. Novo

摘要

We take into consideration the classical saddle point conditions for programming problems involving convex functions, linear affine functions and a convex set constraint. We prove a nonlinear theorem of the alternative, and we discuss the relationships between the Slater constraint qualification and a constraint qualification proposed by Neustadt (Neustadt LW. Academic Press, New York, pp 323–348,1970) .