This paper investigates the complexity of steepest descent algorithms for two classes of discrete convex functions, M-convex functions and L-convex functions. Simple tie-breaking rules yield complexity bounds that are polynomials in the dimension of the variables and the size of the effective domain. Combination of the present results with a standard scaling approach leads to an efficient algor...

Abstract In this paper, we investigate convex semigroups on Banach lattices with order continuous norm, having $$L^p$$ Lp -spaces in mind as a typical application. We show that the basic results from linear $$C_0$$ xmlns:mml="http://www.w3.org/1998/Math/MathML"><m...

Let X be a topological space and R be a subring of RX. By determining some special topologies on X associated with the subring R, characterizations of maximal fixxed and maximal growing ideals in R of the form Mx(R) are given. Moreover, the classes of zR-ideals and z0R-ideals are introduced in R which are topological generalizations of z-ideals and z0-ideals of C(X), respectively. Various c...

This paper consider the   general  forms of $(alpha,beta)$-fuzzyleft ideals (right ideals, bi-ideals, interior ideals) of an orderedsemigroup, where$alpha,betain{in_{gamma},q_{delta},in_{gamma}wedgeq_{delta}, in_{gamma}vee q_{delta}}$ and $alphaneqin_{gamma}wedge q_{delta}$. Special attention is paid to$(in_{gamma},ivq)$-left ideals (right ideals, bi-ideals, interiorideals) and some related  pr...

We consider reasoning and minimization in systems of polynomial ordinary differential equations (odes). The ring of multivariate polynomials is employed as a syntax for denoting system behaviours. We endow polynomials with a transition system structure based on the concept of Lie derivative, thus inducing a notion ofL-bisimulation. Two states (variables) are provenL-bisimilar if and only if the...

After the introduction of fuzzy set by Zadeh in 1965 [1], there have been a number of generalizations of this fundamental concept. In 1967, Goguen [2] proposed the concept of L-fuzzy set. The idea of interval valued fuzzy set is given by Zadeh in 1975 [3]. Type 2 fuzzy sets were poposed by Zadeh in [4]. Attanasove introduced intuitionistic fuzzy sets in 1986 [5]. Interval valued intuitionistic ...

The first step towards near-rings was an axiomatic research done by Dickson in 1905. In 1936, it was Zassenhaus who used the name near-ring. Many parts of the well established theory of rings are transferred to near-rings and new specific features of near-rings have been discovered. To deal with the idea of near-rings using ternary product Warud Nakkhasen and Bundit Pibaljommee have applied the...

This paper sheds a new light on submodular function minimization and maximization from the viewpoint of discrete convex analysis. L-convex functions and M-concave functions constitute subclasses of submodular functions on an integer interval. Whereas L-convex functions can be minimized efficiently on the basis of submodular (set) function minimization algorithms, M-concave functions are identif...