In many data mining applications, it is a priori known that the target function should satisfy certain constraints imposed by, for example, economic theory or a human-decision maker. In this paper we consider partially monotone prediction problems, where the target variable depends monotonically on some of the input variables but not on all. We propose a novel method to construct prediction mod...

Monotone operators are of basic importance in optimization as they generalize simultaneously subdifferential operators of convex functions and positive semidefinite (not necessarily symmetric) matrices. In 1970, Asplund studied the additive decomposition of a maximal monotone operator as the sum of a subdifferential operator and an “irreducible” monotone operator. In 2007, Borwein and Wiersma [...

We deal with monotone inclusion problems of the form 0 ∈ Ax+Dx+NC(x) in real Hilbert spaces, where A is a maximally monotone operator, D a cocoercive operator and C the nonempty set of zeros of another cocoercive operator. We propose a forwardbackward penalty algorithm for solving this problem which extends the one proposed by H. Attouch, M.-O. Czarnecki and J. Peypouquet in [3]. The condition ...

It is widely believed that if monotone difference schemes are applied to the linear convection equation with discontinuous initial data, then solutions of the monotone schemes are closer to solutions of their parabolic modified equations than that of the original convection equation. We will confirm the conjecture in this paper. It is well known that solutions of the monotone schemes and their ...

A geometric graph is angle-monotone if every pair of vertices has a path between them that—after some rotation—is xand ymonotone. Angle-monotone graphs are √ 2-spanners and they are increasing-chord graphs. Dehkordi, Frati, and Gudmundsson introduced anglemonotone graphs in 2014 and proved that Gabriel triangulations are angle-monotone graphs. We give a polynomial time algorithm to recognize an...

Amonotone drawing of a planar graph G is a planar straightline drawing of G where a monotone path exists between every pair of vertices of G in some direction. Recently monotone drawings of planar graphs have been proposed as a new standard for visualizing graphs. A monotone drawing of a planar graph is a monotone grid drawing if every vertex in the drawing is drawn on a grid point. In this pap...

We introduce a new representation class of Boolean functions|monotone term decision lists|which combines compact representation size with tractability of essential operations. We present many properties of the class which make it an attractive alternative to traditional universal representation classes such as DNF formulas or decision trees. We study the learnability of monotone term decision l...

In this paper, we introduce a new class of monotone operators − (H(·, ·), η)monotone operators, which generalize many existing monotone operators. The resolvent operator associated with an (H(·, ·), η)monotone operator is defined and its Lipschitz continuity is presented. As an application, we also consider a new generalized mixed variational inclusion involving (H(·, ·), η)-monotone operators ...

In this paper, we studied maximal monotonicity of type FPV for sum of two maximal monotone operators of type FPV and the obtained results improve and complete the corresponding results of this filed.

Abstract Monotone matrices are stochastic that satisfy the monotonicity conditions as introduced by Daley in 1968. Markov chains useful modeling phenomena several areas. Most previous work examines embedding problem for within entire set of transition matrices, and only a few studies focus on embeddability specific subset matrices. This article discrete-time monotone chain, i.e., existence matr...