Re: Unable to generate any initial points with NMaximize (or NMinimize)

*To*: mathgroup at smc.vnet.net*Subject*: [mg131073] Re: Unable to generate any initial points with NMaximize (or NMinimize)*From*: Dana DeLouis <dana01 at icloud.com>*Date*: Sun, 9 Jun 2013 04:31:49 -0400 (EDT)*Delivered-to*: l-mathgroup@mail-archive0.wolfram.com*Delivered-to*: l-mathgroup@wolfram.com*Delivered-to*: mathgroup-outx@smc.vnet.net*Delivered-to*: mathgroup-newsendx@smc.vnet.net

Hello. It appears you don't have a response, so I'll give it a try. > a > $MachineEpsilon When you have a constraint such as this, you are saying that a solution of 4.440892*10^-16 is not really zero, and a valid solution. 2*$MachineEpsilon//N 4.440892*10^-16 For optimization problems, using ">" is usually a problem because of limits. I believe one should use ">=" for constraints. If 'a was found to be around 0.000001, the program has to retry with a number smaller than this, yet greater than MachineEpsilon. The next try might be at 0.0000001, etc. There's not really a number smaller than MachineEpsilon (at machine precision of course) so what is the software to do? Try using ">=" equ=1/(0.` +(0.012710615354858255` ... etc //FullSimplify; const={a>=0,b>=0,fm>=0,c>=0,p>=0, fm<=5,0.00009600189408524172` (5-fm)-40.451710009005595` b fm>=0}; {val,sol}=NMaximize[{equ,const},{a,b,fm,c,p},MaxIterations->1000] However, I don't believe this problem has a solution as given. :>~ = = = = = = = = = = HTH :>) Dana DeLouis Mac & Mathematica 9 = = = = = = = = = = On Thursday, May 23, 2013 3:16:08 AM UTC-4, Meike wrote: > I often get the error: > > NMaximize::incst: NMaximize was unable to generate any initial points satisfying the inequality constraints > while there are clearly points satisfying the inequality constraints. For example: > NMaximize[{1/(0.` + (0.012710615354858255` (0.07879657698200958` + > a) (0.000046296899009293725` + > 0.003958158898356454` b) (233.02777267494722` + > 102.02996575509754` fm))/(a (4.892449413727213`*^-6 - > 9.784898827454427`*^-7 fm - 0.4123000838756304` b fm)) + ( > 0.10155110608580004` (0.0367973376747971` + > c) (0.5030193912642286` + 16.257272679476753` b + > 0.0309411917473244` p))/b + ( > 219.22680202984347` (0.03970570642848887` + > 0.013422101464134875` fm) (0.07972967880969935` + > 0.14421246041749264` p))/(fm p)), a > $MachineEpsilon, > b > $MachineEpsilon, fm > $MachineEpsilon, c > $MachineEpsilon, > p > $MachineEpsilon, > > 0.00009600189408524172` (5 - fm) - > > 40.451710009005595` b fm > $MachineEpsilon, fm < 5.`}, {a, b, fm, > > c, p}, MaxIterations -> 1000] > > > > NMaximize::incst: NMaximize was unable to generate any initial points satisfying the inequality constraints {-0.000480009+0.0000960019 fm+40.4517 b fm<0}. The initial region specified may not contain any feasible points. Changing the initial region or specifying explicit initial points may provide a better solution. >> > > > > Clearly there are initial points, for example: > > > > 0.00009600189408524172` (5 - fm) - > > 40.451710009005595` b fm > $MachineEpsilon /. {b -> 0.0007, > > fm -> 0.00003} > > > > True > > > > Also, if I make a more simple example with the same constraint I do not get the same error. I know I could give initial values myself, but since I'm automatically generating many of the optimizations, I would prefer not to. And I would like to understand why I keep getting this error and if there is any way to solve it.