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“…For other problems where f * is not known, the absolute difference between the objective function values of consecutive iterations can be compared with ε f to decide termination. Besides, if (12) does not hold, the algorithm has an alternative stopping rule based on the maximum number of iterations (k max ).…”
Section: Stopping Criteriamentioning
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“…For other problems where f * is not known, the absolute difference between the objective function values of consecutive iterations can be compared with ε f to decide termination. Besides, if (12) does not hold, the algorithm has an alternative stopping rule based on the maximum number of iterations (k max ).…”
Section: Stopping Criteriamentioning
“…Filter methods have been combined with trust-region approaches [2,3], SQP techniques [4,5], inexact restoration algorithms [6,7], interior point strategies [8] and line-search algorithms [9,10,11]. They also have been extended to other areas of optimization such as nonlinear equations and inequalities [12,13,14,15], nonsmooth optimization [16,17], unconstrained optimization [18,19], complementarity problems [20,21] and derivativefree optimization [22,23,24,25].…”
Section: Introductionmentioning
“…We use the BCDF-QNB algorithm [11] in the restoration phase of the DFF algorithm. BCDF-QNB (Box-Constrained Derivative-Free Quasi Newton), based on the Broyden update formula, is a derivative-free method for solving underdetermined nonlinear systems with bound constraints.…”
Section: Restoration Phasementioning
“…The restoration phase must solve an underdetermined nonlinear system with bound constraints. In our implementation we performed this phase using the derivative-free method developed in [11].…”
Section: Introductionmentioning
“…Many of them are combinations of Newton methods with some strategies taking into account the constraint set. Strategies based on projections, trust region, active set and gradient methods have been used; see, e.g., [3,5,10,18,19,20,24,25,26,31,32,33]. A Newton conditional gradient (Newton-CondG) method was proposed in [15] (see [16] for its inexact version) to compute approximate solutions of (3).…”
Section: Introductionmentioning