Using Symbolic function to execute Optimization in MATLAB

Hello all I ran into a symbolic viarible optimization problem in MATLAB. I tried to define array containing with symbolic element, and then apply a certain function and I would like to optimize this function which contain symbolic variables. Error notes show: "Function 'ge' is not implemented for MuPAD symbolic objects" which i assume meaning MATLAB can not run optimization on symbolic object functions. is there anyone know how to fix it? pls.....

This is the code:

clear all  
global N ITERATION_STEP BETA a1 a2 a3
syms a1 a2 a3
N=3;
ITERATION_STEP=3;
% discount factor
BETA=0.95;
prob = [0.662,0.547,0.769];             %prob = rand(1,n);
disp('prob');
disp(prob);
states = zeros(1,N);   
actions = [a1, a2, a3];
%actions(1,:)=20;       initial transmitted power is 20dB
inst_reward = zeros(1,N);  
future_reward = zeros(1,N);
for i = 1:N
    imm_reward = InstReward(prob,actions);
end

disp('imm_reward');
disp(imm_reward);

% at every moment, there are two possible rewards, name them reward1 and
% reward 2 which reward1 denotes the reward when no state change happens,
% while reward2 denotes the reward when state changes. 

for j = 1:2
    for i = 1:2
        alter_prob = 1 - prob;
        reward1 = InstReward(prob, actions);
        reward2 = InstReward(alter_prob, actions);
        total = BETA.^(j)*(prob.*reward1 + alter_prob.*reward2);
        future_reward = imm_reward + sum(total);
    end
end

obj_function = @(actions)(sum(future_reward));
% optimization algorithm to find the value of actions to get the min reward
% [X,FVAL,EXITFLAG,OUTPUT] = fmincon(FUN,X0,A,B,Aeq,Beq,LB,UB,NONLCON,OPTIONS)

%options = optimset('Display','off');
[X,FVAL,EXITFLAG,OUTPUT] = fmincon(obj_function,[0,0],[],[],[],[],0,[]);

But I got error note as: Error using sym>notimplemented (line 2682) Function 'ge' is not implemented for MuPAD symbolic objects.

Error in sym/ge (line 823) notimplemented('ge');

Error in nlconst (line 663) elseif f >=0

Error in fmincon (line 794) [X,FVAL,LAMBDA,EXITFLAG,OUTPUT,GRAD,HESSIAN]=...

Error in main (line 42) [X,FVAL,EXITFLAG,OUTPUT] = fmincon(obj_function,[0,0],[],[],[],[],0,[]);

Answer 1

[Matt J]

No, fmincon (and other Optimization Toolbox solvers) do not do symbolic optimization.

You can use intermediate symbolic computations within your objective function and constraints to help generate output, but all direct input and output arguments to fmincon must be non-symbolic.

Answer 2

[Walter Roberson]

You can use matlabFunction() to generate an anonymous function from a symbolic expression, and then optimize that function.

[viva]

thx a lot. Care to give me an example? coz i am not sure how to use matlabFunction() to pass the function.....

Answer 3

[Alan Weiss]

There are examples in the documentation showing how to optimize using matlabFunction. Here is one, and here is another.

Alan Weiss

MATLAB mathematical toolbox documentation

Answer 4

[viva]

hi all. i revised the code as followed using matlabFunction, but there are still mistakes on the last line:

clear all  
global N ITERATION_STEP BETA a1 a2 a3
syms a1 a2 a3
N=3;
ITERATION_STEP=3;
% discount factor
BETA=0.95;
prob = [0.662;0.547;0.769];             %prob = rand(1,n);
disp('prob');
disp(prob);
states = zeros(N,1);   
actions = [a1; a2; a3];
%actions(1,:)=20;       initial transmitted power is 20dB
inst_reward = zeros(N,1);  
future_reward = zeros(N,1);
for i = 1:N
    imm_reward = InstReward(prob,actions);
end

disp('imm_reward');
disp(imm_reward);

% at every moment, there are two possible rewards, name them reward1 and
% reward 2 which reward1 denotes the reward when no state change happens,
% while reward2 denotes the reward when state changes. 

for j = 1:2
    for i = 1:2
        alter_prob = 1 - prob;
        reward1 = InstReward(prob, actions);
        reward2 = InstReward(alter_prob, actions);
        total = BETA.^(j)*(prob.*reward1 + alter_prob.*reward2);
        future_reward = imm_reward + sum(total);
        f = sum(future_reward);
        obj_function = matlabFunction(f,'vars',{actions});

          % optimization algorithm to find the value of actions to get the min reward
          % [X,FVAL,EXITFLAG,OUTPUT] = fmincon(FUN,X0,A,B,Aeq,Beq,LB,UB,NONLCON,OPTIONS)
          % options = optimset('Display','off');
          [X,FVAL,EXITFLAG,OUTPUT] = fmincon(@obj_function,[0,0],[],[],[],[],0,[]);

      end
  end

Error: File: main.m Line: 52 Column: 45 "obj_function" was previously used as a variable, conflicting with its use here as the name of a function or command.

[Matt J]

Omit the '@',

fmincon(obj_function,...

[viva]

yes, u r right, now i am struggling on this part:

objfun = matlabFunction(f,'vars',{actions});
    constraint = a1+a2+a3-50;
        confun = matlabFunction(constraint);
        % optimization algorithm to find the value of actions to get the min reward
        % [X,FVAL,EXITFLAG,OUTPUT] = fmincon(FUN,X0,A,B,Aeq,Beq,LB,UB,NONLCON,OPTIONS)
        options = optimset('Display','off');
        [X,FVAL,EXITFLAG,OUTPUT] = fmincon(objfun,[0,0,0],[],[],[],[],[],[],confun,options);

and there are error note said: Index exceeds matrix dimensions. Caused by: Failure in initial user-supplied objective function evaluation. FMINCON cannot continue.

Dear Matt, do you know what the problem is here? thx for your help.

[Matt J]

Test your objfun to see if it can accept a length(x)=3 input