Find gradient of objective function for fmincon
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Hello,
I need to optimize 2 points. I am finding it difficult to manually calculate the gradient of the objective function The shortened version of the code is as follows:
W1 = @(X) objfun(X,XQ,YQ,cdf1,cdf2);
% I have a meshgrid, where XQ, YQ, cdf1, cdf2 are of mxn matrix and are known
options = optimoptions('fmincon','Algorithm','sqp', 'Display','iter-detailed',...
'CheckGradients',true,'SpecifyObjectiveGradient',true);
lb = [1909,-390;
2059,-390];
ub = [1969,-360;
2059,-360];
initValue = [1969,-360;
2059,-360];
%these values are not important here
[x1,~,exitflag] = fmincon(W1,initValue,[],[],[],[], lb1, ub1, [], options);
%where
function [f,gradf] = objfun(X,XQ,YQ,cdf1,cdf2)
p1 = @(Point) interp2(XQ,YQ,cdf1,Point(1,1),Point(1,2),'nearest');
p2 = @(Point) interp2(XQ,YQ,cdf2,Point(2,1),Point(2,2),'nearest');
f = -1+(1-p1(X))*(1-p2(X));
if nargout > 1
[gx1, gy1] = gradient(cdf1);
[gx2, gy2] = gradient(cdf2);
dp1x = @(Point) interp2(XQ,YQ,gx1,Point(1,1),Point(1,2),'nearest');
dp1y = @(Point) interp2(XQ,YQ,gy1,Point(1,1),Point(1,2),'nearest');
dp2x = @(Point) interp2(XQ,YQ,gx2,Point(2,1),Point(2,2),'nearest');
dp2y = @(Point) interp2(XQ,YQ,gy2,Point(2,1),Point(2,2),'nearest');
gradfx1 = @(P) - dp1x * (1-p2(P)) ;
gradfy1 = @(P) - dp1y * (1-p2(P)) ;
gradfx2 = @(P) - (1-p1(P)) * dp2x ;
gradfy2 = @(P) - (1-p1(P)) * dp2y ;
gradfx = [gradfx1 ; gradfx2];
gradfy = [gradfy1 ; gradfy2];
gradf = [gradfx;gradfy];
end
end
I get the following error:
Error using vertcat
Nonscalar arrays of function handles are not allowed; use cell arrays instead.
Error in SBR_Optimisation_tool_1_8_4/objfun (line 2893)
gradfx = [gradfx1 ; gradfx2];
I am sure I am not calculating the gradient correctly. I simpy cannot use gradient(f) or gradient(p1). That gives other kinds of error. How to calculate the gradient here?
4 个评论
Torsten
2023-1-11
编辑:Torsten
2023-1-11
p1 = @(x,y) interp2(XQ,YQ,cdf1,x,y,'nearest');
p2 = @(x,y) interp2(XQ,YQ,cdf2,x,y,'nearest');
These two functions are not even continuous functions of x and y. So how could you calculate a gradient for them ?
Further, you must supply numerical values for the gradient at x, not a function handle as you do.
Be happy if fmincon works with your non-differentiable function and don't try to make things even worse by supplying non-existing gradients.
Walter Roberson
2023-1-11
To get around that particular problem change
gradfx = [gradfx1 ; gradfx2];
gradfy = [gradfy1 ; gradfy2];
gradf = [gradfx;gradfy];
to
gradfx = {gradfx1 ; gradfx2};
gradfy = {gradfy1 ; gradfy2};
gradf = [gradfx;gradfy];
The result will be a 4 x 1 cell array of function handles, which is legal in MATLAB.
MATLAB does not permit you to use [] to put more than one function handle into an array, because if it did, gradfx(1) would be ambiguous about whether you are invoking the array of function handles each on the input [1], or if you were invoking each of the function handles with no input and then indexing the result at the first location, or if you were selecting the first function handle to be returned as a function handle, or if you were selecting the first function handle and invoking it with no input. It therefore forces you to store multiple function handles in cell, as you can then use {} and () to control your meaning.
采纳的回答
Matt J
2023-1-11
编辑:Matt J
2023-1-11
Perhaps as follows. Note my restructuring of your array into an Nx2x2 form.
function [f,gradf] = objfun(X,XQ,YQ,cdf1,cdf2)
[x1,y1,x2,y2]=deal(X(:,1,1), X(:,2,1), X(:,1,2), X(:,2,2));
p1 = interp2(XQ,YQ,cdf1,x1,y1,'cubic');
p2 = interp2(XQ,YQ,cdf2,x2,y2,'cubic');
f = -1+(1-p1)*(1-p2);
if nargout > 1
D=1e7*eps(X);
[dx1,dy1,dx2,dy2]=deal(D(:,1,1), D(:,2,1), D(:,1,2), D(:,2,2));
p1x1=(interp2(XQ,YQ,cdf1,x1+dx1,y1,'cubic') -p1)./dx1;
p1y1=(interp2(XQ,YQ,cdf1,dx1,y1+dy1,'cubic') -p1)./dy1;
p2x2=(interp2(XQ,YQ,cdf2,x2+dx2,y2,'cubic') -p2)./dx2;
p2y2=(interp2(XQ,YQ,cdf2,dx2,y2+dy2,'cubic') -p2)./dy2;
gradp1=[p1x1;
p1y1].*(1-p2);
gradp2=[p2x2;
p2y2].*(1-p1);
gradf=[gradp1;gradp2];
end
end
2 个评论
更多回答(1 个)
Walter Roberson
2023-1-11
Using interp2 with 'nearest' is incompatible with fmincon, fminunc, fminsearch, and most of the other optimizers. In particular it is incompatible with any of the gradient based optimizers, all of which require the the first and second derivatives of the equations are continuous. If you need 'nearest' in the objective function then you must switch to ga() or one of a small number of other optimizers. As none of these other optimizers use gradients then the method of calculation of gradient for them becomes irrelevant.
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