Geodesic
Nonmonotone strategy for minimization of quadratics with simple constraints
Applications of Mathematics, Tome 46 (2001) no. 5, pp. 321-338.

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An algorithm for quadratic minimization with simple bounds is introduced, combining, as many well-known methods do, active set strategies and projection steps. The novelty is that here the criterion for acceptance of a projected trial point is weaker than the usual ones, which are based on monotone decrease of the objective function. It is proved that convergence follows as in the monotone case. Numerical experiments with bound-constrained quadratic problems from CUTE collection show that the modified method is in practice slightly more efficient than its monotone counterpart and has a performance superior to the well-known code LANCELOT for this class of problems.
DOI : 10.1023/A:1013752209845
Classification : 65F15, 65K05, 65K10, 90C20, 90C52
Keywords: quadratic programming; conjugate gradients; active set methods 
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     title = {Nonmonotone strategy for minimization of quadratics with simple constraints},
     journal = {Applications of Mathematics},
     pages = {321--338},
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Diniz-Ehrhardt, M. A.; Dostál, Z.; Gomes-Ruggiero, M. A.; Martínez, J. M.; Santos, S. A. Nonmonotone strategy for minimization of quadratics with simple constraints. Applications of Mathematics, Tome 46 (2001) no. 5, pp. 321-338. doi : 10.1023/A:1013752209845. http://geodesic.mathdoc.fr/articles/10.1023/A:1013752209845/

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