Constraint qualifications for nonsmooth programming

Time: 2019-06-25 17:34:35

        For a constrained optimization problem, it is widely concerned under  what assumptions the Karush–Kuhn–Tucker necessary optimality condition holds at the local minimizers. Those assumptions  are often called constraint qualifications. Having many constraint qualifications for smooth optimizations problems, researchers aim to develop more assumptions to nonsmooth problems  or problems defined on general normed spaces or Banach spaces. In this paper, we aim at providing constraint qualifications and the  Karush–Kuhn–Tucker necessary optimality conditions in form of generalized  subdifferentials.

        By using an implicit function theorem and a result of error bound, we provide new constraint qualifications ensuring the Karush–Kuhn–Tuker necessary optimality conditions for both smooth and nonsmooth optimization problems in normed spaces or Banach spaces.

References：

1.Liren Huang, Lulin Tan, Chunguang Liu. Constraint qualifications for nonsmooth programming. Optimization, 67(12), 2139-2155, 2018. DOI: 10.1080/02331934.2018.1546702