Akifumi Kira

Construction of explicit optimal value functions by a symbolic-numeric cylindrical algebraic decomposition

Recently parametric treatment of constraint solving and optimization problems has received considerable attention in science and engineering. In this paper we show an efficient and systematic algorithm for parametric programming, i.e. computing exact optimal value functions, based on a specialized symbolic-numeric cylindrical algebraic decomposition. We also present some practical application examples from system and control theory.

AN APPLICATION OF A DISCRETE FIXED POINT THEOREM TO A GAME IN EXPANSIVE FORM

In this paper, we first present a discrete fixed point theorem for contraction mappings from the product set of integer intervals into itself, which is an extension of Roberts discrete fixed point theorem. Next, we derive an existence theorem of a pure-strategy Nash equilibrium for a noncooperative n-person game from our fixed point theorem. Finally, we show that Kuhns theorem for a game in expansive form can be explained by our existence theorem.

Modeling and Managing Airport Passenger Flow Under Uncertainty: A Case of Fukuoka Airport in Japan

Airport terminal decision makers in recent years need to deal with unexpected and sudden congestion situations. Although various types of mathematical researchs has analyzed the congestion situations and have succeed to manage a subsystem, they cannot sufficiently describe the variety of phenomena observed in a real airport terminal, because they have not considered the interactions between subsystems of the real airport terminal. A simulation approach enables us to describe the interactions between facilities and passenger behavior in detail as a whole airport system and to find various types of possible congestion situations. The simulation approach, however, cannot directly lead exact prediction that can be useful in practical management and operation for difficulties of modeling a complex airport terminal system and acquiring complete input data. In this paper, (1) we modeled Fukuoka airport international terminal in Japan as Complex Adaptive System and built a passenger flow simulation based on the Discrete Event Model. Validity of the model was confirmed by experiments. Moreover, (2) we confirmed that it is possible to acquire simulation input data from discussing with stakeholders using the simulation. Therefore, we believe that it is possible to reduce uncertainty of the model systematically by continuing modeling, predicting, and discussing with stakeholders, repeatedly.

Golden Complementary Dual in Quadratic Optimization

This paper discusses the dual of infinite-variable quadratic minimization (primal) problems from a view point of Golden ratio. We consider two pairs of primal and dual (maximization) problems. One pair yields the Golden complementary duality: (i) Both the minimum value function and the maximum value function are the identical Golden quadratic. (ii) Both the minimum point and the maximum point constitute the Golden paths. (iii) The alternate sequence of both the Golden paths constitutes another Golden path. The other yields the inverse-Golden complementary duality: (i)i¾? Both the minimum value function and the maximum value function are the identical inverse-Golden quad- ratic, (ii) and (iii).