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Nonmonotone spectral projected gradient methods on convex sets
 SIAM Journal on Optimization
, 2000
"... Abstract. Nonmonotone projected gradient techniques are considered for the minimization of differentiable functions on closed convex sets. The classical projected gradient schemes are extended to include a nonmonotone steplength strategy that is based on the Grippo–Lampariello–Lucidi nonmonotone lin ..."
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Cited by 133 (25 self)
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Abstract. Nonmonotone projected gradient techniques are considered for the minimization of differentiable functions on closed convex sets. The classical projected gradient schemes are extended to include a nonmonotone steplength strategy that is based on the Grippo–Lampariello–Lucidi nonmonotone line search. In particular, the nonmonotone strategy is combined with the spectral gradient choice of steplength to accelerate the convergence process. In addition to the classical projected gradient nonlinear path, the feasible spectral projected gradient is used as a search direction to avoid additional trial projections during the onedimensional search process. Convergence properties and extensive numerical results are presented.
Equilibria With Infinitely Many Differentiated Classes Of Customers
, 1997
"... . In this work we consider a bicriterion extension of equilibrium problems formulated as variational inequalities, and propose for its solution a generalization of the FrankWolfe method. Under suitable monotonicity assumptions on the cost function and a reasonable regularity assumption, we prove t ..."
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Cited by 4 (3 self)
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. In this work we consider a bicriterion extension of equilibrium problems formulated as variational inequalities, and propose for its solution a generalization of the FrankWolfe method. Under suitable monotonicity assumptions on the cost function and a reasonable regularity assumption, we prove that the FrankWolfe iterates converge linearly to the unique solution of our equilibrium problem. Key words. Equilibrium, variational inequalities, FrankWolfe algorithm, multiobjective. AMS subject classifications. 47H05, 49J40, 49M27, 90C25 1. Introduction and problem formulation. Consider the problem of determining an equilibrium state resulting from the interaction of infinitely many agents in a system, and assume that the equilibria correspond to the solutions of a finite dimensional variational inequality. More precisely, we say that a vector x in R n is a solution of the variational inequality problem VIP(H,\Omega\Gamma associated with the set\Omega and the function H : R n ! R...