Skipping Invalid Problems in a Pseudo BMI Solver

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Skipping Invalid Problems in a Pseudo BMI Solver

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TOPIC: Skipping Invalid Problems in a Pseudo BMI Solver

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#5802

Skipping Invalid Problems in a Pseudo BMI Solver 1 Year, 7 Months ago Karma: 0

Hi,
I'm having trouble implementing a cheap solver for a simple BMI problem as described in Cogill's paper on Quadratic Approximated Value Functions.

It's a very dirty approach and I'm looking into PENBMI, but I haven't obtained it yet. If there's a better to do this with Yalmip / Sedumi / SDPT3, let me know.

Anyhow, this is what I'm doing:
The bilinearity is limited to a scalar in [0,1], so I'm discretizing this interval and solving an LMI for every point as in the code snippet below.

I'm checking the diagnostics afterwards and set infeasible problems to a very large value to invalidate them when I pick the best result from my results vector.

The problem is that sometimes, Yalmip will throw an error when the constraints aren't really a constraint, but just straight out infeasible or always valid. For example, let A1 = 2; A2 = 0; and rho = 0.75
Then the constraint is essentially:
Y >= Q + Y
which is always true (with the non-variable Qs I'm using).

Code:



for(rho_idx = 1:length(0:hstep:1))

    obj = trace(WVar * Y) + rho*lambda;

    constr = [Y>=0];

    constr = [constr, Y>=Q+(1-rho)*A1'*Y*A1+rho*A2'*Y*A2];

    diagnostics = solvesdp(constr,obj,sdpsettings('solver','sdpt3','verbose',0));

end

I get the following error for this example:

Code:

??? Undefined function or method 'is' for input arguments of type 'double'.



Error in ==> lmi.lmi at 142

    if is(Fi{1},'sos')



Error in ==> constraint.set at 52

    F = lmi(varargin{1});



Error in ==> constraint.horzcat at 14

        F=F+set(varargin{i});



Error in ==> ETC_Cog_YSearchTh1 at 23

        constr = [constr, Y>=Q+(1-rho)*A1'*Y*A1+rho*A2'*Y*A2];



Error in ==> mk_test_1D_overall at 24

[CogQuadEst_thresh,Y_out,rho_out] = ETC_Cog_YSearchTh1(A1,A2,G, lambda, WVar);

inde

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#5804

Re: Skipping Invalid Problems in a Pseudo BMI Solver 1 Year, 7 Months ago Karma: 32

Yes, it fails if that happens

This reproduces it
Y = sdpvar(2)
[Y>0, Y>Y]

It is fixed in the next release. In case you don't want to code around it (simply check if the expression is a double, recommended approach since if it is infeasib le, YALMIP will simply not solve the problem but generate an error during construction of constraint), here is the very messy fix that should replace the code around line 34 in @constraint/constraint

Code:



if isa(Z,'double')

    

    if  size(Z,1)==size(Z,2) &&  norm(Z-Z',inf)<1e-12 && ~isequal(quantifier,'==')

        checkSDP = 1;

    else

        checkSDP = 0;

    end

    

    if checkSDP

        if min(eig(Z))>=0

            warning('Constraint evaluated to trivial true.')

            F = [];

            return

        else

            error('SDP constraint evaluated to trivial false (no decision variable in constraint)')            

        end

    else

        Z = Z(:);

        switch quantifier

            case '=='

                if all(Z)==0

                    warning('Constraint evaluated to trivial true.')

                    F = [];

                    return

                else

                    error('Equality constraint evaluated to trivial false (no decision variable in constraint)')

                end

            case {'<=','>='}

                if all(Z>=0)

                    warning('Constraint evaluated to trivial true.')

                    F = [];

                    return

                else

                    error('Inequality constraint evaluated to trivial false (no decision variable in constraint)')

                end

            case {'<','>'}

                if all(Z>0)

                    warning('Constraint evaluated to trivial true.')

                    F = [];

                    return

                else

                    error('Inequality constraint evaluated to trivial false (no decision variable in constraint)')

                end

        end

    end

end

lofberg

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Posts: 2280

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#5809

Re: Skipping Invalid Problems in a Pseudo BMI Solver 1 Year, 7 Months ago Karma: 0

Thank you so much for your reply.

I guess I'll code around it.

Code:



    if( isa(Y>=Q+(1-rho)*A1'*Y*A1+rho*A2'*Y*A2, 'double') )        

            temp_ret(rho_idx) = BIG_M;

            continue;

    else

        constr = [constr, Y>=Q+(1-rho)*A1'*Y*A1+rho*A2'*Y*A2];

    end

didn't quite work as the condition doesn't fire when the problem appears. Is this not the way to check for double here?

inde

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Posts: 3

Last Edit: 2011/10/12 09:53 By inde.

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#5812

Re: Skipping Invalid Problems in a Pseudo BMI Solver 1 Year, 7 Months ago	Karma: 32
isa(Y-(Q+(1-rho)A1'YA1+rhoA2'YA2), 'double')

lofberg

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#5814

Re: Skipping Invalid Problems in a Pseudo BMI Solver 1 Year, 7 Months ago	Karma: 0
thanks so much. This works (unsurprisingly for you most probably)

inde

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