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An example of SDPs (semidenite programs) exhibits a substantial diculty in proving the superlinear convergence of a direct extension of the Mizuno-Todd-Ye type predictor-corrector primal-dual interior-point method for LPs (linear programs) to SDPs, and suggests that we need to force the generated sequence to converge to a solution tangentially to the… (More)
This paper proposes a globally convergent predictor-corrector infeasible-interior-point algorithm for the monotone semidenite linear complementarity problem using the Alizadeh-Haeberly-Overton search direction, and shows its quadratic local convergence under the strict complementarity condition.
In this paper, we study some basic properties of the monotone semidenite nonlinear complementarity problem (SDCP). We show that the trajectory continuously accumulates into the solution set of the SDCP passing through the set of the infeasible but positive denite matrices under certain conditions. Especially, for the monotone semide-nite linear… (More)
Various search directions used in interior-point-algorithms for the SDP (semidef-inite program) and the monotone SDLCP (semidenite linear complementarity problem) are characterized by the intersection of a maximal monotone ane subspace and a maximal and strictly antitone ane subspace. This observation provides a unied geometric view over the existence of… (More)
This paper proposes a new predictor-corrector interior-point method for a class of semidefinite programs, which numerically traces the central trajectory in a space of Lagrange multipliers. The distinguished features of the method are full use of the BFGS quasi-Newton method in the corrector procedure, and an application of the conjugate gradient method… (More)
Let C be a full dimensional, closed, pointed and convex cone in a nite dimensional real vector space E with an inner product hx; yi of x; y 2 E, and M a maximal monotone subset of E 2 E. This paper studies the existence and continuity of centers of the monotone generalized complementarity problem associated with C and M: Find (x; y) 2 M \ (C 2 C 3) such… (More)
Allergen-specific immunotherapy has been applied to canine atopic dermatitis. Despite the accumulated clinical evidence of its effect for atopic dogs, the basic immunologic mechanisms were not fully understood. In this study, the cytokine profile ex vivo in canine atopic dermatitis before and after allergen-specific immunotherapy was characterized using… (More)
A new proof of Euler's formula for polytopes is presented via an approach using potential functions. In particular, a connection between Euler's formula and the Morse relation from differential topology is established.