Yoshiyuki Sekiguchi

Regularity estimates for convex multifunctions

The main result of the paper contains an exact formula for the rate of regularity of a set-valued mapping with a convex graph. As a consequence we find an exact expression for the rate of regularity of set-valued mappings associated with so-called constraint systems. It turns out that the rate is equal to the upper bound of Robinson-type estimates over all norms in the graph space of the homogenized mapping majorizing the norm of the underlying space. We further introduce a concept of a perfectly regular mapping and find some criteria for perfect regularity.

Average-case competitive analyses for one-way trading

Consider a trader who exchanges one dollar into yen and assume that the exchange rate fluctuates within the interval [m,M]. The game ends without advance notice, then the trader is forced to exchange all the remaining dollars at the minimum rate m. El-Yaniv et al. presented the optimal worst-case threat-based strategy for this game (El-Yaniv et al. 2001). In this paper, under the assumption that the distribution of the maximum exchange rate is known, we provide average-case analyses using all the reasonable optimization measures and derive different optimal strategies for each of them. Remarkable differences in behavior are as follows: Unlike other strategies, the average-case threat-based strategy that minimizes E[OPT/ALG] exchanges little by little. The maximization of E[ALG/OPT] and the minimization of E[OPT]/E[ALG] lead to similar strategies in that both exchange all at once. However, their timing is different. We also prove minimax theorems with respect to each objective function.

Collision Probability in an Automated Production Line under Erlang Distribution

Flat panel displays (FPDs) are manufactured through many different processing equipments arranged sequentially in a line. Although the constant inter-arrival time (i.e., the tact time) of glass substrates in the line should be kept as short as possible, the collision probability between glass substrates increases as the time becomes shorter. Since the glass substrate is expensive and fragile, the collision should be avoided. In this paper, we derive a closed form formula of the collision probability for a model, in which the processing time on each equipment is assumed to follow the Erlang distribution. We also show some numerical results and computer simulation results of the collision probability.

Exact estimates of regularity modulus for infinite programming

An exact estimate on the modulus of metric regularity for linear systems is given. By applying the estimate, we obtain explicit forms of the modulus for linear conical systems and differentiable nonlinear systems on the space of continuous functions.

Real Radicals and Finite Convergence of Polynomial Optimization Problems

Polynomial optimization appears various areas of mathematics. Although it is a fully nonlinear nonconvex optimization problems, there are numerical algorithms to approximate the global optimal value by generating sequences of semidefinite programming relaxations. In this paper, we study how real radicals of ideals have roles in duality theory and finite convergence property. Especially, duality theory is considered in the case that the truncated quadratic module is not necessarily closed. We will also try to explain the results by giving concrete examples.

An improved analysis of SRPT scheduling algorithm on the basis of functional optimization

The competitive performance of the SRPT scheduling algorithm has been open for a long time except for being 2-competitive, where the objective is to minimize the total completion time. Chung et al. proved that the SRPT algorithm is 1.857-competitive. In this paper we improve their analysis and show a 1.792-competitiveness. We clearly mention that our result is not the best so far, since Sitters recently proved the algorithm is 1.250-competitive. Nevertheless, it is still well worth reporting our analytical method; our analysis is based on the modern functional optimization, which can scarcely be found in the literature on the analysis of algorithms. Our aim is to illustrate the potentiality of functional optimization with a concrete application.

Average-Case Competitive Analyses for One-Way Trading

Consider a trader who exchanges one dollar into yen and assume that the exchange rate fluctuates within the interval [m,M]. The game ends without advance notice, then the trader is forced to exchange all the remaining dollars at the minimum rate m. El-Yaniv et al presented the optimal worst-case threat-basedstrategy (WTB) for this game [4].In this paper, under the assumption that the distribution of the maximum exchange rate is known, we provide average-case analyses using all the reasonable optimization measures and derive different optimal algorithms for each of them. Remarkable differences in behavior are as follows: Unlike other algorithms, the average-case threat-basedstrategy (ATB) that minimizes

Exact Formulae for Regularity Estimates

E[\text{OPT} / \text{ALG}]

Real ideal and the duality of semidefinite programming for polynomial optimization

exchanges little by little. The maximization of

Collision Probability in an In-Line Equipment Model under Erlang Distribution

E [\text{ALG} / \text{OPT}]