Sy-Ming Guu

Asymptotic methods for aggregate growth models

Abstract We use perturbation methods to compute optimal policy functions in simple continuous- and discrete-time aggregate growth models. We demonstrate that computing the kth degree Taylor expansion of the policy function around the steady state involves solving one quadratic equation and k − 1 linear equations. We also compute Pade expansions, and show that both Taylor and Pade expansions can provide excellent solutions far from the steady state.

MINIMIZING A LINEAR OBJECTIVE FUNCTION WITH FUZZY RELATION EQUATION CONSTRAINTS

An minimization problem with a linear objective function subject to fuzzy relation equations using max-product composition has been considered by Loetamonphong and Fang. They first reduced the problem by exploring the special structure of the problem and then proposed a branch-and-bound method to solve this 0-1 integer programming problem. In this paper, we provide a necessary condition for an optimal solution of the minimization problems in terms of one maximum solution derived from the fuzzy relation equations. This necessary condition enables us to derive efficient procedures for solving such optimization problems. Numerical examples are provided to illustrate our procedures.

Minimizing a linear function under a fuzzy max–min relational equation constraint

In this paper we investigate the problem of minimizing a linear objective function subject to a fuzzy relational equation constraint. A necessary condition for optimal solution is proposed. Based on this necessary condition, we propose three rules to simplify the work of computing an optimal solution. Numerical examples are provided to illustrate the procedure. Experimental results are reported showing that our new procedure systematically outperforms our previous work.

Asymptotic methods for asset market equilibrium analysis

Summary. General equilibrium analysis is difficult when asset markets are incomplete. We make the simplifying assumption that uncertainty is small and use bifurcation methods to compute Taylor series approximations for asset demand and asset market equilibrium. A computer must be used to derive these approximations since they involve large amounts of algebraic manipulation. We use this method to analyze the allocative and welfare effects of introducing a new security. We find that adding any nontrivial derivative security will raise the price of the risky security relative to the bond when risks are small.

An accelerated approach for solving fuzzy relation equations with a linear objective function

In literature, the optimization model with a linear objective function subject to fuzzy relation equations has been converted into a 0-1 integer programming problem by Fang and Li (1999). They proposed a jump-tracking branch-and-bound method to solve this 0-1 integer programming problem. In this paper, we propose an upper bound for the optimal objective value. Based on this upper bound and rearranging the structure of the problem, we present a backward jump-tracking branch-and-bound scheme for solving this optimization problem. A numerical example is provided to illustrate our scheme. Furthermore, testing examples show that the performance of our scheme is superior to the procedure in the paper by Fang and Li. Several testing examples show that our initial upper bound is sharp.

Weighted coefficients in two-phase approach for solving the multiple objective programming problems

Abstract Two-phase approach with equal weighted coefficients has been proposed to yield an efficient solution for multiple objective programming problems. In this note, we will show that the two-phase approach, as long as the weighted coefficients are positive, not necessarily equal, will generate an efficient solution. A counterexample is given to the case that some weighted coefficients are zero.

Perturbation Solution Methods for Economic Growth Models

Economic growth is one of the most important macroeconomic phenomena. With economic growth comes the possibility of improving the living standards of all in a society. Economic growth has been studied by all generations of economists. Economists have used optimal control theory and dynamic programming to formalize the study of economic growth, yielding many important insights. Unfortunately, most of these methods are generally qualitative and do not yield the kind of precise quantitative solutions necessary for econometric analysis and policy analysis.

A Note on Fuzzy Relation Programming Problems with Max-Strict- t -Norm Composition

The fuzzy relation programming problem is a minimization problem with a linear objective function subject to fuzzy relation equations using certain algebraic compositions. Previously, Guu and Wu considered a fuzzy relation programming problem with max-product composition and provided a necessary condition for an optimal solution in terms of the maximum solution derived from the fuzzy relation equations. To be more precise, for an optimal solution, each of its components is either 0 or the corresponding components value of the maximum solution. In this paper, we extend this useful property for fuzzy relation programming problem with max-strict-t-norm composition and present it as a supplemental note of our previous work.

On the Optimal Three-tier Multimedia Streaming Services

In this paper, we provide a mathematical model for the streaming media provider seeking a minimum cost while fulfilled the requirements assumed by a three-tier framework. The proposed model involves a linear cost function subjected to fuzzy relational equations, where the algebraic operations employed are the max-min operations.

Finding Common Solutions of a Variational Inequality, a General System of Variational Inequalities, and a Fixed-Point Problem via a Hybrid Extragradient Method

We propose a hybrid extragradient method for finding a common element of the solution set of a variational inequality problem, the solution set of a general system of variational inequalities, and the fixed-point set of a strictly pseudocontractive mapping in a real Hilbert space. Our hybrid method is based on the well-known extragradient method, viscosity approximation method, and Mann-type iteration method. By constrasting with other methods, our hybrid approach drops the requirement of boundedness for the domain in which various mappings are defined. Furthermore, under mild conditions imposed on the parameters we show that our algorithm generates iterates which converge strongly to a common element of these three problems.