Book review: Aniko Magashazi (2021). Singapore Globally Entangled. Lessons for Central Europe? K?szeg: Institute of Advanced Studies K?szeg (iASK), 310, ISBN 978-615-5742-15-6 Aniko Magashazi’s monograph provides an analysis that is embedded in a thorough and well-constructed discussion the major salient features Singapore. The novelty topic as evident today it was evaluated by author al...

An optimal algorithm is presented for computing the smallest set of linear inequalities that define the integer hull of a possibly unbounded two-dimensional convex polygon R. Input to the algorithm is a set of linear inequalities defining R, and the integer hull computed is the convex hull of the integer points of R. It is proven that the integer hull has at most O(n logAmax) inequalities, wher...

Let A and B be n n positive semidefinite Hermitian matrices, let c and/ be real numbers, let o denote the Hadamard product of matrices, and let Ak denote any k )< k principal submatrix of A. The following trace and eigenvalue inequalities are shown: tr(AoB) <_tr(AoBa), c_<0or_> 1, tr(AoB)a_>tr(AaoBa), 0_a_ 1, A1/a(A o Ba) <_ Al/(Az o B), a <_ /,a O, Al/a[(Aa)k] <_ A1/[(A)k], a <_/,a/ 0. The equ...

In this note we present inequalities relating the successive minima of a o-symmetric convex body and the successive inner and outer radii of the body. These inequalities build a bridge between known inequalities involving only either the successive minima or the successive radii.

Let f(d) = (fs, fi, . . . . fd,) be the f-vector of a Cohen-Macaulay complex A. Bjijrner proved that (*) fief++, for any O<ii[d/2] and (**) f0 Q fi < < fr+ i rP1. Recently, Stanley generalized Bjorner’s inequalities (*) and (**) for pure simplicial complexes. In this paper we consider O-sequence analogue of the inequalities (*) and (**). Let (ha, h,, . . . . h,), h,#O, is a pure O-sequence. We ...

Valid inequalities for 0-1 knapsack polytopes often prove useful when tackling hard 0-1 Linear Programming problems. To use such inequalities effectively, one needs separation algorithms for them, i.e., routines for detecting when they are violated. We show that the separation problems for the so-called extended cover and weight inequalities can be solved exactly in O(nb) time and O((n+ amax)b)...

Abstract. The function that maps a positive semidefinite matrix to the trace of one of its nonnegative integer power is semidefinite representable. In this note, we reduce the size of this semidefinite representation from O(kn) linear matrix inequalities of dimension n, where k is the desired power and n× n the size of the matrix to O(log 2 (k)) linear matrix inequalities of dimension 2n. We al...

In this paper we derive efficiency estimates of the regularized Newton’s method as applied to constrained convex minimization problems and to variational inequalities. We study a one-step Newton’s method and its multistep accelerated version, which converges on smooth convex problems as O( 1 k3 ), where k is the iteration counter. We derive also the efficiency estimate of a second-order scheme ...