Nonlinear programming - ib qho ntawm lub Cheebtsam ntawm zauv programming

Nonlinear programming yog ib feem ntawm zauv programming, nyob rau hauv uas ib tug uas tsis yog-linear muaj nuj nqi yog sawv cev los ntawm tej yam xyuas los yog lub hom phiaj muaj nuj nqi. Lub ntsiab yam khoom ntawm lub nonlinear programming yog mus nrhiav lub zoo nqi ntawm lub hom phiaj kev ua muab ib tug tej yam muaj pes tsawg tus ntawm tsis thiab xyuas.

uas tsis yog-linear programming teeb meem yog txawv los ntawm cov teeb meem ntawm linear ntsiab lus pom tau tsis tsuas tsis pub dhau lub cheeb tsam, uas muaj ib co kev txwv, tab sis kuj txawv teb chaws. Cov teeb meem yog cov uas xyuam xim programming kev pab raws qib uas yuav tsum tau muaj tuaj raws li cov equations thiab inequalities.

Nonlinear Programming yog txwv kom muab zais raws li cov nuj nqi ntau yam F (x), muaj nuj nqi txwv thiab ua tus dimension ntawm lub vector x. Yog li, lub npe ntawm tus neeg ua hauj lwm nyob rau hauv lub xov tooj ntawm cov tsiaj ntawv. Thaum siv ib tug nce mus nce los nonlinear programming yuav ua tau ntawm ib tug-parameter unconstrained optimization. Yog hais tias cov xov tooj ntawm cov tsiaj ntawv koj yuav tau siv ntau tshaj ib tug unconditional multi-parameter optimization.

Yuav kom daws tau cov teeb meem linearity siv txheem txoj kev linear programming (e.g., simplex txujci). Tab sis nrog tus qauv ntawm cov tshuaj tsis muaj nyob nonlinear, xaiv nyob rau hauv txhua tus neeg cov ntaub ntawv thiab nws tseem yog nws nyob rau cov nuj nqi F (x).

Nonlinear programming tshwm sim nyob rau hauv lub neej txhua hnub ntau heev. Piv txwv li, nws yog ib tug disproportionate nce nyob rau hauv cov nqi kom muaj nuj nqis ua los muas khoom.

Tej zaum nrhiav txoj kev pom kev daws teeb meem nyob rau hauv nonlinear programming teeb meem sim mus ua ib tug approximation rau linear teeb meem. Ib qho piv txwv yog lub quadratic programming, nyob rau hauv uas cov nuj nqi F (x) yog sawv cev los ntawm ib tug polynomial ntawm ob degree nrog rau kev hwm mus lub zog, lub cai linearity cov kev txwv. Ib tug thib ob piv txwv yog lub siv ntawm lub txim ua txoj kev, cov kev siv ntawm cov uas nyob rau hauv tej yam kev txwv thiaj li muaj cov searching rau extremum analogous txoj kev tsis muaj tej kev txwv solved ntau yooj yim dua.

Txawm li cas los, thaum analyzed raws li ib tug tag nrho, uas tsis yog-linear programming yog cov tshuaj rau ntau zog computational teeb meem ntawm cov neeg ua hauj lwm. Heev feem ntau peb siv cov approximate kev daws teeb meem thaum lub sij hawm lawv optimization hom kev kawm. Lwm lub cuab tam haib uas yuav tsum tau muaj los daws tau qhov yam teeb meem - hais txog zauv txoj kev mus nrhiav tus txoj kev hais haum mus rau ib tug muab cov neeg.

Raws li hais saum toj no, uas tsis yog-linear programming yuav tsum tau ib tug tshwj xeeb ib tug neeg mus kom ze, uas yuav tsum coj mus rau hauv tus account nws tseem.

Muaj cov nram qab no txoj kev nonlinear programming:

- Gradient txoj kev, raws li nyob rau hauv cov khoom ntawm kev haumxeeb gradient nyob rau hauv point. Nyob rau hauv lwm yam lus, cov vector ntawm ib nrab derivatives xam nyob rau hauv lub taw tes coj raws li cov kev taw qhia ntawm ntau index ua zog nyob rau hauv lub cheeb tsam ntawm no taw tes.

- Monte Carlo txoj kev, nyob rau hauv uas lub parallelepiped txiav txim n-th dimension, xws li ib tug plurality ntawm kev pab them nqi rau tom ntej modeling random N-dots nrog teeb tis nyob rau hauv lub parallelepiped.

- txoj kev ntawm dynamic programming yog txo mus rau ib tug ntau txoj optimization teeb meem kev pab raws qib rau ib tug me dimension.

- convex programming txoj kev yog siv nyob rau hauv cov kev tshawb fawb rau qhov tsawg kawg nkaus ntawm ib tug convex muaj nuj nqi los yog ib tug tshaj plaws ntawm ib tug concave rau lub convex ib feem ntawm lub teeb lub hom phiaj. Nyob rau hauv lub rooj plaub uas ib tug plurality ntawm kev pab them nqi yog ib tug convex polyhedron, ces tej zaum nws yuav tsum muaj ntaub ntawv yooj yim txoj kev.