The local resolvent set of a locally Lipschitzian transformation is open

The Resolvent of a Closed Transformation

Locally Lipschitzian Guiding Function Method for ODEs

by generalizing the well known guiding function method. Such an approach can be found in several works, however, under some heavier assumptions. For example, in [M] f is assumed to be locally lipschitzian and the guiding function to be C. In [GP] f needs to be of the Caratheodory type only, while the corresponding guiding function must be still C. In fact, in [GP] the more general, multivalued ...

A Local Branching Approach for the Set Covering Problem

The set covering problem (SCP) is a well-known combinatorial optimization problem. This paper investigates development of a local branching approach for the SCP. This solution strategy is exact in nature, though it is designed to improve the heuristic behavior of the mixed integer programming solver. The algorithm parameters are tuned by design of experiments approach. The proposed method is te...

Hermitian Geometry on Resolvent Set

For a tuple A = (A1, A2, ..., An) of elements in a unital Banach algebra B, its projective joint spectrum P (A) is the collection of z ∈ C such that A(z) = z1A1 +z2A2 + · · ·+znAn is not invertible. It is known that the B-valued 1-form ωA(z) = A−1(z)dA(z) contains much topological information about the joint resolvent set P (A). This paper defines Hermitian metric on P (A) through the B-valued ...

Resolvent Clause Weighting Local Search

Considerable progress in local search has recently been made in using clause weighting algorithms to solve satisfiability benchmark problems. While these algorithms have outperformed earlier stochastic techniques on many larger problems, this improvement has generally required extra, problem specific, parameters requiring fine tuning to problem domains for optimal run-time performance. In a pre...