We develop monotone iterative technique for a system of semilinear elliptic boundary value problems when the forcing function is the sum of Caratheodory functions which are nondecreasing and nonincreasing, respectively. The splitting of the forcing function leads to four different types of coupled weak upper and lower solutions. In this paper, relative to two of these coupled upper and lower so...

We give an fpt approximation algorithm for the directed vertex disjoint cycle problem. Given a directed graph G with n vertices and a positive integer k, the algorithm constructs a family of at least k/ρ(k) disjoint cycles of G if the graph G has a family of at least k disjoint cycles (and otherwise may still produce a solution, or just report failure). Here ρ is a computable function such that...

Numerical solutions of 2× 2 semilinear systems of elliptic boundary value problems, whose nonlinearities are of quasimonotone nondecreasing, quasimonotone nonincreasing, or mixed quasimonotone types, are computed. At each step of the (quasi) monotone iteration, the solution is represented by a simple-layer potential plus a domain integral; the simple-layer density is then discretized by boundar...

We consider the two-bar charts packing problem which is a generalization of strongly NP-hard bin and 2-D vector problem. propose an O(n2.5)-time 16/11-approximation algorithm for when at least one bar each chart has height more than 1/2 5/4-approximation nonincreasing or nondecreasing higher 1/2.

The minimax identity for a nondecreasing upper-semicontinuous utility function satisfying mild growth assumption is studied. In contrast to the classical setting, concavity of not asumed. By considering concave envelope function, equalities and inequalities between robust functionals an initial its concavification are obtained. Furthermore, similar proved in case implementing upper bound on fin...

An optimal control problem is considered where a risky asset is used for investment, and this investment is financed by initial wealth as well as by a state dependent income. The objective function is accumulated discounted expected utility of wealth, where the utility function is nondecreasing and bounded. This problem is investigated for constant as well as for stochastic discount rate, where...

The Perceptron algorithm elegantly solves binary classification problems that have a margin between positive and negative examples. Isotonic regression (fitting an arbitrary increasing function in one dimension) is also a natural problem with a simple solution. By combining the two, we get a new but very simple algorithm with strong guarantees. Our ISOTRON algorithm provably learns Single Index...

We present a simple approach to study the one–dimensional pressureless Euler system via adhesion dynamics in the Wasserstein space P2(R) of probability measures with finite quadratic moments. Starting from a discrete system of a finite number of “sticky” particles, we obtain new explicit estimates of the solution in terms of the initial mass and momentum and we are able to construct an evolutio...

Numerical solutions of 2× 2 semilinear systems of elliptic boundary value problems, whose nonlinearities are of quasimonotone nondecreasing, quasimonotone nonincreasing, or mixed quasimonotone types, are computed. At each step of the (quasi) monotone iteration, the solution is represented by a simple-layer potential plus a domain integral; the simple-layer density is then discretized by boundar...

A rigorous decomposition-based approach for solution of nonseparable mixedinteger nonlinear programs involving factorable nonconvex functions is presented. The proposed algorithm consists of solving an alternating sequence of Relaxed Master Problems (a Mixed-Integer Linear Program) and nonlinear programming problems. The number of major iterations can be significantly decreased by use of piecew...