In this article, we provide a splitting method for solving monotone inclusions in real Hilbert space involving four operators: maximally monotone, monotone-Lipschitzian, cocoercive, and monotone-continuous operator. The proposed takes advantage of the intrinsic properties each operator, generalizing forward–backward–half-forward Tseng’s algorithm with line search. At iteration, our defines step...

For classification problems with ordinal attributes very often the class attribute should increase with each or some of the explanatory attributes. These are called classification problems with monotonicity constraints. Standard classification tree algorithms such as CART or C4.5 are not guaranteed to produce monotone trees, even if the data set is completely monotone. We look at pruning based ...

We prove tight lower bounds, of up to n , for the monotone depth of functions in monotone-P. As a result we achieve the separation of the following classes. 1. monotone-NC 6 = monotone-P. 2. For every i 1, monotone-NC i 6 = monotone-NC i+1. 3. More generally: For any integer function D(n), up to n (for some > 0), we give an explicit example of a monotone Boolean function, that can be computed b...

We study the complexity of approximating monotone Boolean functions with disjunctive normal form (DNF) formulas, exploring two main directions. First, we construct DNF approximators for arbitrary monotone functions achieving one-sided error: we show that every monotone f can be ε-approximated by a DNF g of size 2n−Ωε( √ n) satisfying g(x) ≤ f(x) for all x ∈ {0, 1}. This is the first non-trivial...

This paper proposes new notions of polynomial depth (called monotone poly depth), based on a polynomial version of monotone Kolmogorov complexity. We show that monotone poly depth satisfies all desirable properties of depth notions i.e., both trivial and random sequences are not monotone poly deep, monotone poly depth satisfies the slow growth law i.e., no simple process can transform a non dee...

The classes of monotone or convex (and necessarily monotone) densities on ℝ(+) can be viewed as special cases of the classes of k-monotone densities on ℝ(+). These classes bridge the gap between the classes of monotone (1-monotone) and convex decreasing (2-monotone) densities for which asymptotic results are known, and the class of completely monotone (∞-monotone) densities on ℝ(+). In this pap...

This paper deals with numerical solving semilinear parabolic problems based on the method of upper and lower solutions. A monotone iterative method with quadratic convergence rate is constructed. The monotone iterative method combines an explicit construction of initial upper and lower solutions and the modified accelerated monotone iterative method. The monotone iterative method leads to the e...