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 ...

3. page 13, lines 12–13: Insert a phrase to stress that we consider only monotone LCP in this book, though the qualifier ”monotone” is often omitted. Replace the sentence preceding the formula (1.21) by The monotone LCP—the qualifier ”monotone” is implicit throughout this book—is the problem of finding vectors x and s in I R that satisfy the following conditions: 4. page 13, line −12: delete “o...

In this paper we propose a new large-update primal-dual interior point algorithm for P∗( ) linear complementarity problems (LCPs). We generalize Bai et al.’s [A primal-dual interior-point method for linear optimization based on a new proximity function, Optim. Methods Software 17(2002) 985–1008] primal-dual interior point algorithm for linear optimization (LO) problem to P∗( ) LCPs. New search ...

The rediscovery of the affine scaling method in the late 80s was one of the turning points which led to a new chapter in Modern Optimization the Interior Point Methods (IPMs). The purpose of this paper is to show the intrinsic connections between Interior and Exterior Point methods (EPMs), which have been developed during the last 30 years. A class Ψ of smooth and strictly concave functions ψ :...

We extend the uniqueness and simplicity results of Cuntz and Krieger to the countably infinite case, under a row-finite condition on the matrix A. Then we present a new approach to calculating the K-theory of the Cuntz-Krieger algebras, using the gauge action of T, which also works when A is a countably infinite 0 − 1 matrix. This calculation uses a dual Pimsner-Voiculescu six-term exact sequen...

In a recent paper, Dipper and Doty, [2], introduced certain finite dimensional algebras, associated with the natural module of the general linear group and its dual, which they call rational Schur algebras. We give a proof, via tilting modules, that these algebra are in fact generalized Schur algebras. Using the same technique we show that certain finite dimensional algebras with classical grou...

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Kumar described the Schubert classes which are the dual to the closures of the Bruhat cells in the flag varieties of the Kac-Moody groups associated to the infinite dimensional KacMoody algebras [17]. These classes are indexed by affine Weyl groups and can be chosen as elements of integral cohomologies of the homogeneous space L̂polGC/B̂ for any compact simply connected semisimple Lie groupG. Lat...

Let k be an algebraically closed field of characteristic p. We shall discuss the cohomology algebras of a block ideal B of the group algebra kG of a finite group G and a block ideal C of the block ideal of kH of a subgroup H of G which are in Brauer correspondence and have a common defect group, continuing [4]. We shall define a (B,C)-bimodule L. The k-dual L∗ induces the transfer map between t...

In this paper the abstract of the thesis ”New Interior Point Algorithms in Linear Programming” is presented. The purpose of the thesis is to elaborate new interior point algorithms for solving linear optimization problems. The theoretical complexity of the new algorithms are calculated. We also prove that these algorithms are polynomial. The thesis is composed of seven chapters. In the first ch...