Convergence property of the Iri-Imai algorithm for some smooth convex programming problems

In this paper, the Iri-Imai algorithm for solving linear and convex quadratic programming is extended to solve some other smooth convex programming problems. The globally linear convergence rate of this extended algorithm is proved, under the condition that the objective and constraint functions satisfy a certain type of convexity, called the harmonic convexity in this paper. A characterization of this convexity condition is given. The same convexity condition was used by Mehrotra and Sun to prove the convergence of a path-following algorithm. The Iri-Imai algorithm is a natural generalization of the original Newton algorithm to constrained convex programming. Other known convergent interior-point algorithms for smooth convex programming are mainly based on the path-following approach

A D-induced duality and its applications

This paper attempts to extend the notion of duality for convex cones, by basing it on a predescribed conic ordering and a fixed bilinear mapping. This is an extension of the standard definition of dual cones, in the sense that the nonnegativity of the inner-product is replaced by a pre-specified conic ordering, defined by a convex cone D, and the inner-product itself is replaced by a general multi-dimensional bilinear mapping. This new type of duality is termed the D-induced duality in the paper. We further introduce the notion of D-induced polar sets within the same framework, which can be viewed as a generalization of the D-induced polar sets within the same framework, which can be viewed as a generalization of the D-induced dual cones and are convenient to use for some practical applications. Properties of the extended duality, including the extended bi-polar theorem, are proven. Furthermore, attention is paid to the computation and approximation of the D-induced dual objects. We discuss, as examples, applications of the newly introduced D-induced duality concepts in robust conic optimization and the duality theory for multi-objective conic optimization

Matrix convex functions with applications to weighted centers for semidefinite programming

In this paper, we develop various calculus rules for general smooth matrix-valued functions and for the class of matrix convex (or concave) functions first introduced by Loewner and Kraus in 1930s. Then we use these calculus rules and the matrix convex function -log X to study a new notion of weighted convex centers for semidefinite programming (SDP) and show that, with this definition, some known properties of weighted centers for linear programming can be extended to SDP. We also show how the calculus rules for matrix convex functions can be used in the implementation of barrier methods for optimization problems involving nonlinear matrix functions

Low-complexity algorithms for sequencing jobs with a fixed number of job-classes

In this paper we consider the problem of scheduling n jobs such that makespan is minimized. It is assumed that the jobs can be divided into K job-classes and that the change-over time between two consecutive jobs depends on the job-classes to which the two jobs belong. In this setting, we discuss the one machine scheduling problem with arbitrary processing times and the parallel machines scheduling problem with identical processing times. In both cases it is assumed that the number of job-classes K is fixed. By using an appropriate integer programming formulation with a fixed number of variables and constraints, it is shown that these two problems are solvable in polynomial time. For the one machine scheduling case it is shown that the complexity of our algorithm is linear in the number of jobs n. Moreover, if the problem is encoded according to the high multiplicity model of Hochbaum and Shamir, the time complexity of the algorithm is shown to be a polynomial in log n. In the parallel machine scheduling case, it is shown that if the number of machines is fixed the same results hold. Copyrigh

Heuristics for the 0-1 Min-Knapsack Problem

The 0-1 min-knapsack problem consists in finding a subset of items such that the sum of their sizes is larger than or equal to a given constant and the sum of their costs is minimized. We first study a greedy-type heuristic having a worst-case bound of 2. This heuristic is then refined to obtain a new one with a worst-case bound of 3/2

Checkpoint kinase 2-mediated phosphorylation of BRCA1 regulates the fidelity of nonhomologous end-joining

The tumor suppressor gene BRCA1 maintains genomic integrity by protecting cells from the deleterious effects of DNA double-strand breaks (DSBs). Through its interactions with the checkpoint kinase 2 (Chk2) kinase and Rad51, BRCA1 promotes homologous recombination, which is typically an error-free repair process. In addition, accumulating evidence implicates BRCA1 in the regulation of nonhomologous end-joining (NHEJ), which may involve precise religation of the DSB ends if they are compatible (i.e., error-free repair) or sequence alteration upon rejoining (i.e., error-prone or mutagenic repair). However, the precise role of BRCA1 in regulating these different subtypes of NHEJ is not clear. We provide here the genetic and biochemical evidence to show that BRCA1 promotes error-free rejoining of DSBs in human breast carcinoma cells while suppressing microhomology-mediated error-prone end-joining and restricting sequence deletion at the break junction during repair. The repair spectrum in BRCA1-deficient cells was characterized by an increase in the formation of >2 kb deletions and in the usage of long microhomologies distal to the break site, compared with wild-type (WT) cells. This error-prone repair phenotype could also be revealed by disruption of the Chk2 phosphorylation site of BRCA1, or by expression of a dominant-negative kinase-dead Chk2 mutant in cells with WT BRCA1. We suggest that the differential control of NHEJ subprocesses by BRCA1, in concert with Chk2, reduces the mutagenic potential of NHEJ, thereby contributing to the prevention of familial breast cancers

Role of Organic Cation Transporter 1, OCT1 in the Pharmacokinetics and Toxicity of cis-Diammine(pyridine)chloroplatinum(II) and Oxaliplatin in Mice

PurposeThe goal of this study was to test the hypothesis that by controlling intracellular uptake, organic cation transporter 1, Oct1 is a key determinant of the disposition and toxicity of cis-diammine(pyridine)chloroplatinum(II)(CDPCP) and oxaliplatin.MethodsPharmacokinetics, tissue accumulation and toxicity of CDPCP and oxaliplatin were compared between Oct1-/- and wild-type mice.ResultsAfter intravenous administration, hepatic and intestinal accumulation of CDPCP was 2.7-fold and 3.9-fold greater in Oct1 wild-type mice (p < 0.001). Deletion of Oct1 resulted in a significantly decreased clearance (0.444 ± 0.0391 ml/min*kg versus 0.649 ± 0.0807 ml/min*kg in wild-type mice, p < 0.05) and volume distribution (1.90 ± 0.161 L/kg versus 3.37 ± 0.196 L/kg in wild-type mice, p < 0.001). Moreover, Oct1 deletion resulted in more severe off-target toxicities in CDPCP-treated mice. Histologic examination of the liver and measurements of liver function indicated that the level of hepatic toxicity was mild and reversible, but was more apparent in the wild-type mice. In contrast, the effect of Oct1 on the pharmacokinetics and toxicity of oxaliplatin in the mice was minimal.ConclusionsOur study suggests that Oct1 plays an important role in the pharmacokinetics, tissue distribution and toxicity of CDPCP, but not oxaliplatin

An {Mathematical expression} iteration bound primal-dual cone affine scaling algorithm for linear programmingiteration bound primal-dual cone affine scaling algorithm for linear programming

In this paper we introduce a primal-dual affine scaling method. The method uses a search-direction obtained by minimizing the duality gap over a linearly transformed conic section. This direction neither coincides with known primal-dual affine scaling directions (Jansen et al., 1993; Monteiro et al., 1990), nor does it fit in the generic primal-dual method (Kojima et al., 1989). The new method requires {Mathematical expression} main iterations. It is shown that the iterates follow the primal-dual central path in a neighbourhood larger than the conventional {Mathematical expression} neighbourhood. The proximity to the primal-dual central path is measured by trigonometric functions