A sequence a0, a1, . . . , an of real numbers is said to be unimodal if for some 0 ≤ j ≤ n we have a0 ≤ a1 ≤ · · · ≤ aj ≥ aj+1 ≥ · · · ≥ an, and is said to be log-concave if a 2 i ≥ ai−1ai+1 for all 1 ≤ i ≤ n − 1. Clearly a log-concave sequence of positive terms is unimodal. The reader is referred to Stanley’s survey [10] for the surprisingly rich variety of methods to show that a sequence is l...

Standard boundary or finite element methods for problems of high frequency acoustic scattering by convex polygons have a computational cost that grows in direct proportion to the frequency of the incident wave. Here we present a novel Galerkin boundary element method, using plane wave basis functions on a graded mesh, for which the number of degrees of freedom required to achieve a prescribed l...

This paper presents the new concept of second-order cone approximations for convex conic programming. Given any open convex cone K, a logarithmically homogeneous self-concordant barrier for K and any positive real number r ≤ 1, we associate, with each direction x ∈ K, a second-order cone K̂r(x) containing K. We show that K is the intersection of the second-order cones K̂r(x), as x ranges through ...

In this paper, a new inequality for generalized convex functions which is related to the left side of generalized Hermite-Hadamard type inequality is obtained. Some applications for some generalized special means are also given.

The understanding of inequalities in convexity is crucial for studying local fractional calculus efficiency many applied sciences. In the present work, we propose a new class harmonically convex functions, namely, generalized ψ - id="M2"> s -convex functions based on fractal set technique establishing Hermite-Ha...

A sequence a0, a1, . . . , an of real numbers is said to be unimodal if for some 0 ≤ j ≤ n we have a0 ≤ a1 ≤ · · · ≤ aj ≥ aj+1 ≥ · · · ≥ an, and is said to be log-concave if a 2 i ≥ ai−1ai+1 for all 1 ≤ i ≤ n − 1. Clearly a log-concave sequence of positive terms is unimodal. The reader is referred to Stanley’s survey [10] for the surprisingly rich variety of methods to show that a sequence is l...

Introduction Logarithmic concavity is a property of a sequence of real numbers, occurring throughout algebraic geometry, convex geometry, and combinatorics. A sequence of positive numbers a0,... ,ad is log-concave if a2 i ≥ ai−1ai+1 for all i. This means that the logarithms, log(ai), form a concave sequence. The condition implies unimodality of the sequence (ai), a property easier to visualize:...

We analyze a periodic-review inventory model where the decision maker can buy from either of two suppliers. With the first supplier, the buyer incurs a high variable cost but negligible fixed cost; with the second supplier, the buyer incurs a lower variable cost but a substantial fixed cost. Consequently, ordering costs are piecewise linear and concave. We show that a reduced form of generalize...

in this paper, we consider convex quadratic semidefinite optimization problems and provide a primal-dual interior point method (ipm) based on a new kernel function with a trigonometric barrier term. iteration complexity of the algorithm is analyzed using some easy to check and mild conditions. although our proposed kernel function is neither a self-regular (sr) function nor logarithmic barrier ...

This paper is concerned with mean-square stabilization of single-input Markovian jump linear systems (MJLSs) with logarithmically quantized state feedback. We introduce the concepts and provide explicit constructions of stabilizing mode-dependent logarithmic quantizers together with associated controllers, and a semi-convex way to determine the optimal (coarsest) stabilizing quantization densit...