On an Open Problem Related to the Strict Local Minima of Multilinear Objective Functions
نویسندگان
چکیده
This paper gives a combinatorial proof of a “yes” answer to an open question presented in [1], stated as follows: “given a multilinear polynomial E(x): [0; 1] ! <; is it true that Eb(x) = E(x) b x has a strict local minimum over the discrete set f0;1g for almost all b of sufficiently small norm?” The given combinatorial proof is completed directly by providing a sufficient condition for a conjecture on the strict local minima of multilinear polynomials also postulated in [1] to hold. In addition, a simple counterexample is presented to demonstrate that the conjecture may be not true if the provided sufficient condition is not satisfied.
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