Let P（s, δ） be a sphere plant family described by the transfer function set where the coefficients of the denominator and numerator polynomials are affine in a real uncertain parameter vector δ satisfying the Eucl...Let P（s, δ） be a sphere plant family described by the transfer function set where the coefficients of the denominator and numerator polynomials are affine in a real uncertain parameter vector δ satisfying the Euclidean norm constraint ｜｜δ｜｜〈δ. The concept of stabilizability radius of P（s, δ） is introduced which is the norm bound δs for δ such that every member plant of P（s, δ） is stabilizable if and only if ｜｜δ｜｜〈δs. The stabilizability radius can be simply interpreted as the ＇largest sphere＇ around the nominal plant P（s,θ） such that P（s, δ） is stabilizable. The numerical method and the analytical method are presented to solve the stabilizability radius calculation problem of the sphere plants.展开更多
The Balanced Academic Curriculum Problem （BACP） is a constraint satisfaction problem classified as （Non-deterministic Polynomial-time Hard） NP-Hard. This problem consists in the allocation of courses in the period...The Balanced Academic Curriculum Problem （BACP） is a constraint satisfaction problem classified as （Non-deterministic Polynomial-time Hard） NP-Hard. This problem consists in the allocation of courses in the periods that are part of a curriculum such that the prerequisites are satisfied and the load of courses is balanced for the students. This paper presents the solution for a modified BACP where the academic loads and number of curses may be the same or different for each one of the periods and allows having some courses in a specific period. This problem is modeled as an integer programming problem and is proposed the use of Tabu search with short-term memory for its solution because it is not possible to find solutions for all the instances of this modified problem with an exact method.展开更多
This paper shows that the problem of minimizing a linear fractional function subject to asystem of sup-T equations with a continuous Archimedean triangular norm T can be reduced to a 0-1linear fractional optimization ...This paper shows that the problem of minimizing a linear fractional function subject to asystem of sup-T equations with a continuous Archimedean triangular norm T can be reduced to a 0-1linear fractional optimization problem in polynomial time.Consequently,parametrization techniques,e.g.,Dinkelbach's algorithm,can be applied by solving a classical set covering problem in each iteration.Similar reduction can also be performed on the sup-T equation constrained optimization problems withan objective function being monotone in each variable separately.This method could be extended aswell to the case in which the triangular norm is non-Archimedean.展开更多
This paper investigates the equality-constrained minimization of polynomial functions. Let R be the field of real numbers, and R[x1,..., xn] the ring of polynomials over R in variables x1,..., xn. For an f ∈ R[x1,......This paper investigates the equality-constrained minimization of polynomial functions. Let R be the field of real numbers, and R[x1,..., xn] the ring of polynomials over R in variables x1,..., xn. For an f ∈ R[x1,..., xn] and a finite subset H of R[x1,..., xn], denote by V(f : H) the set {f( ˉα) | ˉα∈ Rn, and h( ˉα) =0, ? h ∈ H}. We provide an effective algorithm for computing a finite set U of non-zero univariate polynomials such that the infimum inf V(f : H) of V(f : H) is a root of some polynomial in U whenever inf V(f : H) = ±∞.The strategies of this paper are decomposing a finite set of polynomials into triangular chains of polynomials and computing the so-called revised resultants. With the aid of the computer algebraic system Maple, our algorithm has been made into a general program to treat the equality-constrained minimization of polynomials with rational coefficients.展开更多
基金Project(JSPS.KAKENHI22560451) supported by the Japan Society for the Promotion of ScienceProject(69904003) supported by the National Natural Science Foundation of ChinaProject(YJ0267016) supported by the Advanced Ordnance Research Supporting Fund of China
文摘Let P（s, δ） be a sphere plant family described by the transfer function set where the coefficients of the denominator and numerator polynomials are affine in a real uncertain parameter vector δ satisfying the Euclidean norm constraint ｜｜δ｜｜〈δ. The concept of stabilizability radius of P（s, δ） is introduced which is the norm bound δs for δ such that every member plant of P（s, δ） is stabilizable if and only if ｜｜δ｜｜〈δs. The stabilizability radius can be simply interpreted as the ＇largest sphere＇ around the nominal plant P（s,θ） such that P（s, δ） is stabilizable. The numerical method and the analytical method are presented to solve the stabilizability radius calculation problem of the sphere plants.
文摘The Balanced Academic Curriculum Problem （BACP） is a constraint satisfaction problem classified as （Non-deterministic Polynomial-time Hard） NP-Hard. This problem consists in the allocation of courses in the periods that are part of a curriculum such that the prerequisites are satisfied and the load of courses is balanced for the students. This paper presents the solution for a modified BACP where the academic loads and number of curses may be the same or different for each one of the periods and allows having some courses in a specific period. This problem is modeled as an integer programming problem and is proposed the use of Tabu search with short-term memory for its solution because it is not possible to find solutions for all the instances of this modified problem with an exact method.
基金supported by the National Science Foundation of the United States under Grant No. #DMI- 0553310
文摘This paper shows that the problem of minimizing a linear fractional function subject to asystem of sup-T equations with a continuous Archimedean triangular norm T can be reduced to a 0-1linear fractional optimization problem in polynomial time.Consequently,parametrization techniques,e.g.,Dinkelbach's algorithm,can be applied by solving a classical set covering problem in each iteration.Similar reduction can also be performed on the sup-T equation constrained optimization problems withan objective function being monotone in each variable separately.This method could be extended aswell to the case in which the triangular norm is non-Archimedean.
基金supported by National Natural Science Foundation of China(Grant No.11161034)
文摘This paper investigates the equality-constrained minimization of polynomial functions. Let R be the field of real numbers, and R[x1,..., xn] the ring of polynomials over R in variables x1,..., xn. For an f ∈ R[x1,..., xn] and a finite subset H of R[x1,..., xn], denote by V(f : H) the set {f( ˉα) | ˉα∈ Rn, and h( ˉα) =0, ? h ∈ H}. We provide an effective algorithm for computing a finite set U of non-zero univariate polynomials such that the infimum inf V(f : H) of V(f : H) is a root of some polynomial in U whenever inf V(f : H) = ±∞.The strategies of this paper are decomposing a finite set of polynomials into triangular chains of polynomials and computing the so-called revised resultants. With the aid of the computer algebraic system Maple, our algorithm has been made into a general program to treat the equality-constrained minimization of polynomials with rational coefficients.
