It is shown that any weakly-skew circuit can be converted into a skew circuit with constant factor overhead, while preserving either syntactic or semantic multilinearity. This leads to considering syntactically multilinear algebraic branching programs (ABPs), which are defined by a natural read-once property. A 2 size lower bound is proven for ordered syntactically multilinear ABPs computing an...

we present a modified version of the infeasible-interior- we present a modified version of the infeasible-interior-point algorithm for monotone linear complementary problems introduced by mansouri et al. (nonlinear anal. real world appl. 12(2011) 545--561). each main step of the algorithm consists of a feasibility step and several centering steps. we use a different feasibility step, which targ...

Given polynomial maps \(f, g \colon \mathbb {R}^{n} \to {R}^{n}\), we consider the complementary problem of finding a vector \(x \in {R}^{n}\) such that $$ f(x) \ge 0, \quad g(x) \text{ and } \langle f(x), \rangle = 0. In this paper, present various properties on solution set problem, including genericity, nonemptiness, compactness, uniqueness as well error bounds with explicit exponents. These...