NLP

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NLA
QRSlv
CMSlv
IPSlv
Opt
NLP
CONOPT
IPOPT
TRON
MINOS
NGSlv
OptSQP
DAE/ODE
IDA
LSODE
DOPRI5
LA
linsolqr
linsol
LP
MakeMPS
Logic
LRSlv

NLP = non-linear programming. These types of solvers are used for optimisation problems where there are multiple solutions and you want to chose the one that gives a maximum or minimum value of some objective function.

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