How can I use gamma function in optimization problem

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Daud 2018-9-25

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https://ww2.mathworks.cn/matlabcentral/answers/420699-how-can-i-use-gamma-function-in-optimization-problem

评论： Michele Carone 2022-11-22

epsilon_c = 10e-9; % unitless
lambda = 1e-3; % seconds
P_t = -30; % dB
d = 10; % m
L_H = 40; % bits
L_U = 16; %bits
M_1 = 10; %dB
N_o = -204; %dB
A_o = 30; %dB
m = 1;
alpha = 3;
%%%Variables for Solution
K = optimvar('K', 1, 1, 'Type', 'integer', 'LowerBound', 0, 'UpperBound', 10);
z = optimvar('z', 1, 1, 'Type', 'integer', 'LowerBound', 0,  'UpperBound',10);
%%%Linear Constraints
L = L_H+(K*L_U); % Packet length
R_b = L/lambda; % minimum bit rate
decisioncons = (K/2) - z <= 0;
beta = ((epsilon_c*gamma(m*z+1))^(1/(m*z))*P_t)\(m*N_o*M_1*A_o*d^alpha);
bandwidthcons = B(2^(R_b/B)-1) <= beta;
%%%Solve the Problem
commm = optimproblem('ObjectiveSense','minimize');
commm.Objective = B;
commm.Constraints.decisioncons = decisioncons;
commm.Constraints.bandwidthcons = bandwidthcons;
options = optimoptions('intlinprog','Display','final');
[commmsol,fval,exitflag,output] = solve(commm,'options',options);
sol = commmsol.B

Error:

Undefined function
'gamma' for input
arguments of type
'optim.problemdef.OptimizationExpression'.

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Matt J 2022-11-22

编辑：Matt J 2022-11-22

在 MATLAB Online 中打开

@Michele Carone No, you can use the gamma function in the solver-based framework, e.g.,

xoptimal=fmincon(@(x) gamma(x).^2, 1,[],[],[],[],0,5)
Local minimum found that satisfies the constraints.

Optimization completed because the objective function is non-decreasing in 
feasible directions, to within the value of the optimality tolerance,
and constraints are satisfied to within the value of the constraint tolerance.
xoptimal = 1.4616

Also, in reecent matlab, you can make it work with the problem-based framework using fcn2optimexpr,

x=optimvar('x','Lower',0,'Upper',5);
GamSquare=fcn2optimexpr(@(z) gamma(z).^2, x);
sol0.x=1;
xoptimal = solve(optimproblem('Objective',GamSquare),sol0).x
Solving problem using fmincon.

Local minimum found that satisfies the constraints.

Optimization completed because the objective function is non-decreasing in 
feasible directions, to within the value of the optimality tolerance,
and constraints are satisfied to within the value of the constraint tolerance.
xoptimal = 1.4616

Michele Carone 2022-11-22

thank you @Matt J, I didn't know this new possibility of recent matlab.

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Answer 1

Matt J 2018-9-25

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编辑：Matt J 2018-9-27

Your bandwidthcons are not linear, so optimproblem is not applicable here. Since there are only 100 combinations of K and z that satisfy the bounds, you should probably just use exhaustive search.

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Walter Roberson 2018-9-26

在 MATLAB Online 中打开

gamma() is not defined for datatype optim.problemdef.OptimizationVariable

The defined arithmetic operations for the datatype are:

 .\ (ldivide) -- only when the variable is on the right side, nonscalar constant left permitted
 -  (minus)
 \  (mldivide) -- only when the variable is on the right side and left side is scalar
 ^  (mpower) -- only variable^2
 /  (mrdivide) -- only when variable is on left side and right side is scalar
 *  (mtimes) -- nonscalar left and right permitted and variable^2 terms permitted as long as total degree of any term does not exceed 2
 +  (plus)
 .^ (power) -- only variable.^2
 ./ (rdivide) -- only when variable is on left side; right side can be non-scalar
 .* (times) -- nonscalar left and right permitted and variable^2 terms permitted as long as total degree of any term does not exceed 2
 -  (uminus, unary minus)
 +  (uplus, unary plus)

Matt J 2018-9-27

编辑：Matt J 2018-9-27

And the reason gamma() is not defined for datatype optim.problemdef.OptimizationVariable is because you are not supposed to be doing any nonlinear operations on it, since optimproblem is only intended for linear programming (prior to R2018b).

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