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## The education testing problem revisited

Venue: | IMA J. Numer. Anal |

Citations: | 1 - 1 self |

### Citations

1620 | Practical Methods of Optimization - Fletcher - 1987 |

1403 |
Geometric algorithms and combinatorial optimization
- Grötschel, Lovász, et al.
- 1993
(Show Context)
Citation Context ...ets. It can be proved that Glunt's method converges globally at linear rate. Discussion on the ellipsoid method is fairly rich in the literature. Far from being complete, we simply mention references =-=[2, 3, 12, 14, 21]-=-. The application of this method to the (ETP) is demonstrated in Section 2. Although the ellipsoid method is known to converge eventually, the iterates (the centers) quite often are unfeasible, and th... |

486 |
A polynomial algorithm in linear programming
- Khachiyan
- 1979
(Show Context)
Citation Context ...ets. It can be proved that Glunt's method converges globally at linear rate. Discussion on the ellipsoid method is fairly rich in the literature. Far from being complete, we simply mention references =-=[2, 3, 12, 14, 21]-=-. The application of this method to the (ETP) is demonstrated in Section 2. Although the ellipsoid method is known to converge eventually, the iterates (the centers) quite often are unfeasible, and th... |

117 |
Iterative solution of problems of linear and quadratic programming," Soviet Mathematics Doklady 8(3
- Dikin
- 1967
(Show Context)
Citation Context ...inner ellipsoids mentioned in Theorem 3.3, the analytic center serves as a good starting point for the so called Dikin's method. 3.4. Dikin's Method. Suppose D (c) is a feasible point. Dikin's method =-=[6]-=- amounts to approximating the (ETP) locally by the following subproblem (33) (34) Maximize e T d� subject to d 2 E(H(D (c) ) ;1 �d (c) ) where d (c) = diag(D (c) )ande := [1�:::�1] T . Optimizing line... |

92 | The ellipsoid method: a survey
- Bland, Goldfarb, et al.
- 1981
(Show Context)
Citation Context ...ets. It can be proved that Glunt's method converges globally at linear rate. Discussion on the ellipsoid method is fairly rich in the literature. Far from being complete, we simply mention references =-=[2, 3, 12, 14, 21]-=-. The application of this method to the (ETP) is demonstrated in Section 2. Although the ellipsoid method is known to converge eventually, the iterates (the centers) quite often are unfeasible, and th... |

84 | Large-scale optimization of eigenvalues.
- Overton
- 1992
(Show Context)
Citation Context ...f a di erentiable matrix function are not themselves di erentiable at points where they coalesce. Furthermore, it has been observed quite so often that at an optimal solution the eigenvalues coalesce =-=[19]-=-. To overcome this di culty we can employ special techniques developed in, for example, [18, 19]. For convex programming problems, however, there are simple and e ective algorithms that do not require... |

78 | Ghaoui, “Method of centers for minimizing generalized eigenvalues
- Boyd, E
- 1993
(Show Context)
Citation Context ...r how to express the positive semi-de nite constraints explicitly with m smooth and convex inequalities i(D) 0 where m is small. Discussion for this class of constraints can be found, for example, in =-=[1, 4, 8, 11, 19]-=-. One naive way of representing (2) is that all its principal minors are non-negative. Such an expression, however, is very expensive. Fletcher has tried to depict the normal cone [8, Formula (4.4)] b... |

75 | On minimizing the maximum eigenvalue of a symmetric matrix,
- Overton
- 1988
(Show Context)
Citation Context ...esce. Furthermore, it has been observed quite so often that at an optimal solution the eigenvalues coalesce [19]. To overcome this di culty we can employ special techniques developed in, for example, =-=[18, 19]-=-. For convex programming problems, however, there are simple and e ective algorithms that do not require smooth constraints or di erentiable objectives. For the above (ETP) in particular, the notion o... |

56 | The formulation and analysis of numerical methods for inverse eigenvalue problems - Friedland, Nocedal, et al. - 1987 |

43 | The Theory of Subgradients and Its Applications to Problems of Optimization, Heldermann Verlag, - Rockafellar - 1981 |

39 |
Self-concordant functions and polynomial time methods in convex programming,”
- Nesterov, Nemirovskii
- 1990
(Show Context)
Citation Context ...3 , the boundary of the feasible domain 3 2 and the level curves of are plotted in Figure 1. We rst derive formulas for the gradient r (D) and the Hessian r2 (D). More general results can be found in =-=[4, 16]-=-. Lemma 3.1. The gradient vector of (D) is given by (28) r (D) =diag ; (S ; D) ;1 ; D ;1 : Proof. The derivatives of the second term in (27) is trivial. So the only concern is the partial derivative o... |

32 |
Cut-off method with space extension in convex programming problems. Cyberneticsand Systems Analysis
- SHOR
- 1977
(Show Context)
Citation Context |

21 | Linear Controller Design.
- Boyd, Barratt
- 1991
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Citation Context |

15 |
A nonlinear programming problem in statistics (educational testing
- FLETCHER
- 1981
(Show Context)
Citation Context ...much easier than that in [8]. The convergence property isnumerically demonstrated.s1. Introduction. The educational testing problem (ETP) is a nonlinear programming problem which arises in statistics =-=[7]-=-. The problem is to determine how much can be subtracted from the diagonal of a given symmetric and positive de nite matrix S such that the resulting matrix is positive semi-de nite. The (ETP) can be ... |

7 |
1995], An alternating projection method for certain linear problems in a Hilbert space
- Glunt
- 1995
(Show Context)
Citation Context ...e is that the solution to each subproblem is readily obtainable. It should be mentioned that recently Glunt has proposed another approach to the (ETP) on the basis of an alternating projection method =-=[11]-=-. A major component in Glunt's method is the use of Dkystra's algorithm [5] for computing projections onto the intersection of convex sets. It can be proved that Glunt's method converges globally at l... |

4 |
Optimization over the positive semi-de nite cone: interiorpoint methods and combinatorial applications
- Alizadeh
- 1992
(Show Context)
Citation Context ...r how to express the positive semi-de nite constraints explicitly with m smooth and convex inequalities i(D) 0 where m is small. Discussion for this class of constraints can be found, for example, in =-=[1, 4, 8, 11, 19]-=-. One naive way of representing (2) is that all its principal minors are non-negative. Such an expression, however, is very expensive. Fletcher has tried to depict the normal cone [8, Formula (4.4)] b... |

2 |
A method for nding projections onto the intersection of convex sets in Hilbert space
- Boyle, Dykstra
- 1986
(Show Context)
Citation Context ...e mentioned that recently Glunt has proposed another approach to the (ETP) on the basis of an alternating projection method [11]. A major component in Glunt's method is the use of Dkystra's algorithm =-=[5]-=- for computing projections onto the intersection of convex sets. It can be proved that Glunt's method converges globally at linear rate. Discussion on the ellipsoid method is fairly rich in the litera... |

2 |
Semide nite matrix constraints in optimization
- Fletcher
- 1985
(Show Context)
Citation Context ...ble. Attention is paid to the Dikin's method where a special barrier function and interior ellipsoids for the feasible domain are explicitly formulated. The implementation is much easier than that in =-=[8]-=-. The convergence property isnumerically demonstrated.s1. Introduction. The educational testing problem (ETP) is a nonlinear programming problem which arises in statistics [7]. The problem is to deter... |

1 |
A simpli ed global convergence proof of the a ne scaling algorithm
- Monteiro, Tsuchiya, et al.
- 1992
(Show Context)
Citation Context ...mide nite yet trace(D) mayhave not reached its maximal value. Indeed, one di culty in implementing Dikin's method is that, in contrast to the ellipsoid methods, there is no general stopping criterion =-=[15]-=-. To reduce the risk of hitting boundaries of the feasible domain too soon, we nd it is a good idea to start out the Dikin's method from a point thatismostinterior to the feasible domain. Our numerica... |

1 |
Lower bounds for the reliability of a test
- Woodhouse
- 1976
(Show Context)
Citation Context ...nter, for example, is always a good starting point. 4. Numerical Experiment. We have applied the algorithms discussed in this paper to solve the set of educational testing problems given by Woodhouse =-=[22]-=-. The Woodhouse data set is in general an N m matrix X =[xij] where xij gives the score of student i on subject j. Test problems are generated by selecting various subsets of columns for form the matr... |