We analyze minimization algorithms for L\-convex functions in discrete convex analysis, and establish exact bounds for the number of iterations required by the steepest descent algorithm and its variants.

This project has two main purposes; the first is to perform deciduous-coniferous classification for 65 trees by using the leaf-on single flight LiDAR data. It was done by looking at the geometrical properties of the crown shapes (spherical, conical or cylindrical), these shapes were developed by a rule-driven method Lindenmayer Systems (L systems). Two more parameters that are data driven (conv...

Let E(k, l) denote the smallest integer such that any set of at least E(k, l) points in the plane, no three on a line, contains either an empty convex polygon with k vertices or an empty pseudo-triangle with l vertices. The existence of E(k, l) for positive integers k, l ≥ 3, is the consequence of a result proved by Valtr [Discrete and Computational Geometry, Vol. 37, 565–576, 2007]. In this pa...

Aproximity theorem is astatement that, given an optimization problem and its relaxation, an optimal solution to the original problem exists in acertain neighborhood of asolution to the relaxation. Proximity theorems have been used successfully, for example, in designing efficient algorithms for discrete resource allocation problems. After reviewing the recent results for $\mathrm{L}$-convex and...

In this paper we find a characterization type result for (η1,η2)-convex functions. The Fejér integral inequality related to (η1,η2)-convex functions is obtained as a generalization of Fejér inequality related to the preinvex and η-convex functions. Also some Fejér trapezoid and midpoint type inequalities are given in the case that the absolute value of the derivative of considered function is (...

we first obtain some properties of a fundamentally nonexpansive self-mapping on a nonempty subset of a banach space and next show that if the banach space is having the opial condition, then the fixed points set of such a mapping with the convex range is nonempty. in particular, we establish that if the banach space is uniformly convex, and the range of such a mapping is bounded, closed and con...

In this talk, we focus on a convex risk measure which is induced by the shortfall risk, which is defined as the weighted expectation by some loss function of the positive part of the difference between a claim and a portfolio value at the maturity of our market. The convex risk measure concerned in this talk expresses the least cost to suppress its shortfall risk below the threshold being deter...

The main purpose of this paper is to introduce the compatibility of $M$-fuzzifying topologies and $M$-fuzzifying convexities, define an $M$-fuzzifying topological convex space, and give a method to generate an $M$-fuzzifying topological convex space. Some characterizations of $M$-fuzzifying topological convex spaces are presented. Finally, the notion of $M$-fuzzifying weak topologies is obtaine...

This paper concerns parameterized convex infinite (or semi-infinite) inequality systems whose decision variables run over general infinite-dimensional Banach (resp. finite-dimensional) spaces and that are indexed by an arbitrary fixed set T . Parameter perturbations on the right-hand side of the inequalities are measurable and bounded, and thus the natural parameter space is l∞(T ). Based on ad...