Clarke Generalized Jacobian of the Projection onto Symmetric Cones and Its Applications
نویسندگان
چکیده
In this paper, we give an exact expression for Clarke generalized Jacobian of the projection onto symmetric cones, which is linked to rank-1 matrices. As an application, we employ the projection operator to design a semismooth Newton algorithm for solving nonlinear symmetric cone programs. The algorithm is proved to be locally quadratically convergent without assuming strict complementarity of the solution.
منابع مشابه
Clarke Generalized Jacobian of the Projection onto Symmetric Cones
This paper focuses on Clarke generalized Jacobian of the projection onto symmetric cones. First, we recall some basic concepts. Let ̥ : Ω ⊆ X → Y be a locally Lipschitz function on an open set Ω, where X and Y are two finite dimensional inner product spaces over the field R. Let ∇̥(x) denote the derivative of ̥ at x if ̥ is differentiable at x. The Clarke generalized Jacobian of ̥ at x is defined by...
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