fmincon nonlinear constrain problem set-up

One of my initial conditions is leaving me scratching my head. Since R & C are defined by summing functions (R will have w components and C will have d components), it may be simpliest to represent R & C as functions. Since there is a function f embedded in R, I run in to problems. I can see how to establish the A,b,Aeq and beq inputs, but I have no clue how to represent the nonlinear constraint of f and pass it in to R. Any help would be much appreciated.

    P=R-C; % Objective Function
    -P <= 0;
    R= sum(U*f(sum(sqrt(((Xb+X)-Xw)^2)));
    C= sum(Md*(X-Xb)+B);
    f=@d h*exp(1/d);

Answer 1

[Matt J]

Something like the following, perhaps?

Pfun=@(X) objectiveFull(X, Xb,Xw, U Md,B,h);

nonlcon=@(X) nonlconFull(X,Pfun);

Xopt = fmincon(Pfun,X0, A,b,Aeq,beq,[],[],nonlcon)

       function P=objectiveFull(X,Xb,Xw, U Md,B,h)

          f=@(d) h*exp(1/d);
          R= sum(U*f( norm(X-(Xw-Sb) ) ) );
          C= sum(Md*(X-Xb)+B);

          P=R-C; 

       function [c,ceq]=nonlconFull(X,Pfun)

          ceq=[];
          c=-Pfun(X);

[Matt J]

You could also make objectiveFull and nonlconFull into Nested Functions. This will make it so that they both have access to all the constant parameters simultaneously and can call each other.

[Alec Jeffery]

Great suggestions. I ended up using your nested functions with some modifications (code below). I changed the sign on the constraint function and the objective function. The results seem to be what I want.

% X=x
% Xb=tempBeePos
% Xw=tempWalkerPos
% U=UnitRewards;
% M=BeeAdj(:,1)
% B=BeeAdj(:,2)
% DistRewardFunc
function [Profit,Xopt]=newOptiCode(tempBeePos,tempWalkerPos,UnitRewards,BeeAdj,DistRewardFunc)
M=BeeAdj(:,1);
B=BeeAdj(:,2);
Pfun=@(x) -objectiveFull(x,tempBeePos,tempWalkerPos,UnitRewards,M,B,DistRewardFunc);
% Threw a '-' before function so that you are finding the minimum of -Max
nonlcon=@(x) nonlconFull(x,Pfun);
options = optimoptions('fmincon','Display','off');

Xopt = fmincon(Pfun,tempBeePos, [],[],[],[],[],[],nonlcon,options);
% Xopt = fmincon(Pfun,tempBeePos, A,b,Aeq,beq,[],[],nonlcon)

      function P=objectiveFull(x,tempBeePos,tempWalkerPos,UnitRewards,M,B,DistRewardFunc)
          R=[];
          for w=1:size(tempWalkerPos,1)
              f=DistRewardFunc{w};
              BWdist=sum(sqrt(((tempBeePos+x)-tempWalkerPos(w,:)).^2));
              R(w,1)=UnitRewards(w)*f(BWdist);
          end
          R=sum(R);
          % R= sum(U*f( norm(X-(Xw-Xb) ) ) );
          % C= sum(Md*(X-Xb)+B);
          C=[];
          for d=1:size(tempBeePos,2)
              if x(d) > 0;
              C(d,1)=M(d)*(x(d)-tempBeePos(d))+B(d);
              else
              C(d,1)=B(d);    
              end
          end
          C=sum(C);

          P=R-C;
      end

      function [c,ceq]=nonlconFull(x,Pfun)
          ceq=[];
          c=Pfun(x);
          % changed the sign on c=-Pfun(x)
      end

Profit=objectiveFull(Xopt,tempBeePos,tempWalkerPos,UnitRewards,M,B,DistRewardFunc);

end

[Matt J]

Glad it worked out, but the purpose of my suggestion to use nested functions was to spare you the long argument lists. Below, the nested functions Pfun and nonlcon both share access to the workspace of newOptiCode, so there is no longer any need to pass extra arguments to them (like tempWalkerPos, etc...).

function [Profit,Xopt]=newOptiCode(tempBeePos,tempWalkerPos,...
                        UnitRewards,BeeAdj,DistRewardFunc)

    M=BeeAdj(:,1);
    B=BeeAdj(:,2);

   Xopt = fmincon(@(x) -Pfun(x),tempBeePos, [],[],[],[],...
                        [],[],@nonlcon,options);

   Profit=Pfun(Xopt);

     function P=Pfun(x)
          R=[];
          for w=1:size(tempWalkerPos,1)
              f=DistRewardFunc{w};
              BWdist=sum(sqrt(((tempBeePos+x)-tempWalkerPos(w,:)).^2));
              R(w,1)=UnitRewards(w)*f(BWdist);
          end
          R=sum(R);
          % R= sum(U*f( norm(X-(Xw-Xb) ) ) );
          % C= sum(Md*(X-Xb)+B);
          C=[];
          for d=1:size(tempBeePos,2)
              if x(d) > 0;
              C(d,1)=M(d)*(x(d)-tempBeePos(d))+B(d);
              else
              C(d,1)=B(d);    
              end
          end
          C=sum(C);

          P=R-C;
      end

      function [c,ceq]=nonlcon(x)
          ceq=[];
          c=-Pfun(x);
          % changed the sign on c=-Pfun(x)
      end

end