arXiv subjects

Takashi Tsuchiya

Publications and source records attributed to Takashi Tsuchiya.

22 records · Page 2Linked to original sources

arXiv2015

Weak Infeasibility in Second Order Cone Programming

The objective of this work is to study weak infeasibility in second order cone programming. For this purpose, we consider a relaxation sequence of feasibility problems that mostly preserve the feasibility status of the original problem. This is used to show that for a given weakly infeasible problem at most $m$ directions are needed to approach the cone, where $m$ is the number of Lorentz cones. We also tackle a closely related question and show that given a bounded optimization problem satisfying Slater's condition, we may transform it into another problem that has the same optimal value but it is ensured to attain it. From solutions to the new problem, we discuss how to obtain solution to the original problem which are arbitrarily close to optimality. Finally, we discuss how to obtain finite certificate of weak infeasibility by combining our own techniques with facial reduction. The analysis is similar in spirit to previous work by the authors on SDPs, but a different approach is required to obtain tighter bounds.

math.OC↗

arXiv2015

A structural geometrical analysis of weakly infeasible SDPs

In this article, we present a geometric theoretical analysis of semidefinite feasibility problems (SDFPs). This is done by decomposing a SDFP into smaller problems, in a way that preserves most feasibility properties of the original problem. With this technique, we develop a detailed analysis of weakly infeasible SDFPs to understand clearly and systematically how weak infeasibility arises in semidefinite programming. In particular, we show that for a weakly infeasible problem over $n\times n$ matrices, at most $n-1$ directions are required to approach the positive semidefinite cone. We also present a discussion on feasibility certificates for SDFPs and related complexity results.

math.OC↗

arXiv2013

Logistic Growth for the Nuzi Cuneiform Tablets: Analyzing Family Networks in Ancient Mesopotamia

We reconstruct the year of publication of each cuneiform tablet of the Nuzi society in ancient Mesopotamia. The tablets, are on land transaction, marriage, loan, slavery contracts etc. The number of tablets seem to increase by logistic growth until saturation. It may show the dynamics of concentration of lands or other properties into few powerful families in a period of about twenty years. We reconstruct family trees and social networks of Nuzi and estimate the publication years of cuneiform tablets consistently with the trees and networks, formulating least squares problems with linear inequality constraints.

stat.AP↗

arXiv2013

Double Precision Computation of the Logistic Map Depends on Computational Modes of the Floating-point Processing Unit

Today's most popular CPU can operate in two different computational modes for double precision computations. This fact is not very widely recognized among scientific computer users. The present paper reports the differences the modes bring about using the most thoroughly studied system in chaos theory, the logistic map. Distinct virtual periods due to finite precision come about depending on the computational modes for the parameter value corresponding to fully developed chaos. For other chaotic regime various virtual periods emerge depending on the computational modes and the mathematical expressions of the map. Differences in the bifurcation diagrams due to the modes and the expressions are surveyed exhaustively. A quantity to measure those differences is defined and calculated.

nlin.CD↗