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- W1998081129 abstract "We present a rigorous and comprehensive survey on extensions to the multicriteria setting of three well-known scalar optimization algorithms. Multiobjective versions of the steepest descent, the projected gradient and the Newton methods are analyzed in detail. At each iteration, the search directions of these methods are computed by solving real-valued optimization problems and, in order to guarantee an adequate objective value decrease, Armijo-like rules are implemented by means of a backtracking procedure. Under standard assumptions, convergence to Pareto (weak Pareto) optima is established. For the Newton method, superlinear convergence is proved and, assuming Lipschitz continuity of the objectives second derivatives, it is shown that the rate is quadratic" @default.
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- W1998081129 date "2014-12-01" @default.
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- W1998081129 title "A SURVEY ON MULTIOBJECTIVE DESCENT METHODS" @default.
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- W1998081129 doi "https://doi.org/10.1590/0101-7438.2014.034.03.0585" @default.
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