Full-Newton step polynomial-time methods for LO based on locally ...
Full-Newton step polynomial-time methods for LO based on locally ...
Full-Newton step polynomial-time methods for LO based on locally ...
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• Self-c<strong>on</strong>cordant (barrier) functi<strong>on</strong>sOutline– Definiti<strong>on</strong>s– <str<strong>on</strong>g>Newt<strong>on</strong></str<strong>on</strong>g> <str<strong>on</strong>g>step</str<strong>on</strong>g> and proximity measure– Algorithm with full <str<strong>on</strong>g>Newt<strong>on</strong></str<strong>on</strong>g> <str<strong>on</strong>g>step</str<strong>on</strong>g>s– Complexity analysis– Minimizati<strong>on</strong> of a linear functi<strong>on</strong> over a c<strong>on</strong>vex domain– Algorithm with full <str<strong>on</strong>g>Newt<strong>on</strong></str<strong>on</strong>g> <str<strong>on</strong>g>step</str<strong>on</strong>g>s– Complexity analysis• Kernel-functi<strong>on</strong>-<str<strong>on</strong>g>based</str<strong>on</strong>g> approach– Linear optimizati<strong>on</strong> via self-dual embedding– Central path of self-dual problem– Kernel-functi<strong>on</strong>-<str<strong>on</strong>g>based</str<strong>on</strong>g> barrier functi<strong>on</strong>s– Complexity results• Local self-c<strong>on</strong>cordancy of kernel-functi<strong>on</strong>-<str<strong>on</strong>g>based</str<strong>on</strong>g> barrier functi<strong>on</strong>s• Analysis of the full <str<strong>on</strong>g>Newt<strong>on</strong></str<strong>on</strong>g> <str<strong>on</strong>g>step</str<strong>on</strong>g> method• C<strong>on</strong>cluding remarks• Some references2