Title
On an open problem related to the strict local minima of multilinear objective functions
Document Type
Article
Publication Date
12-1-1997
Abstract
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]n → ℜ, is it true that Eb(x) = E(x) -bℓx has a strict local minimum over the discrete set {0,1}n 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 counter example is presented to demonstrate that the conjecture may be not true if the provided sufficient condition is not satisfied.
Publication Source (Journal or Book title)
IEEE Transactions on Automatic Control
First Page
1564
Last Page
1566
Recommended Citation
Liang, X., & Wu, L. (1997). On an open problem related to the strict local minima of multilinear objective functions. IEEE Transactions on Automatic Control, 42 (11), 1564-1566. https://doi.org/10.1109/9.649717