optimization problem in matlab
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so i want to numerically minimize an expression in the maximims norm.
i have the following code:
function [c1, c2] = minimize_expression(alpha)
fun = @(c) expression_to_minimize(c, alpha);
% Define the initial guess for the optimization
x0 = [0.5, 1];
% Define the lower and upper bounds for the optimization
lb = [0, 0];
ub = [1, Inf];
% Set options for fmincon
options = optimoptions('fmincon', 'Display', 'off', 'Algorithm', 'interior-point', ...
'OptimalityTolerance', 1e-12, 'ConstraintTolerance', 1e-12, ...
'StepTolerance', 1e-12, 'MaxFunctionEvaluations', 1e5, ...
'FunctionTolerance', 1e-12, 'MaxIterations', 1e5, ...
'SpecifyObjectiveGradient', false, 'SpecifyConstraintGradient', false, ...
'HonorBounds', true, 'SubproblemAlgorithm', 'cg', 'CheckGradients', false, ...
'Diagnostics', 'off', 'FiniteDifferenceStepSize', [], 'TypicalX', []);
[c, fval] = fmincon(fun, x0, [], [], [], [], lb, ub, [], options);
% Return the values of c1 and c2
c1 = c(1);
c2 = c(2);
end
function val = expression_to_minimize(c, alpha)
% Define the function whose infinity norm we want to minimize
x = linspace(0, 50, 1001);
f = c(1) * integral(@(t) t^(alpha-1)./cosh(t).*(x.^2.*cos(x))./(x.^2+t.^2), 0, Inf) ...
+ (1-c(1)) * integral(@(t) t^alpha./sinh(t).*(x.*sin(x))./(x.^2+t.^2), 0, Inf) - c(2) * sin(x);
val = norm(f, Inf);
end
however it always produces an error. Any idea whats wrong? Sorry for the format i dont know how to paste code.
4 个评论
Cris LaPierre
2023-2-22
Please share the full error message (copy/paste all the red text).
What is the value of alpha?
david
2023-2-22
John D'Errico
2023-2-22
Remember that infinite domains of integration are often highly problematic. Before you do anything at all, verify that the integrals you are computing do yield meaningful results, for a variety of values for alpha.
Next, when you say that something always return an error, tell us EXACTLY what the error was! So everything in red. Otherwise we cannot know if you are even properly running the code.
david
2023-2-22
回答（1 个）
Why using 'FiniteDifferenceStepSize'and'TypicalX'in your options if you don't want to set values for them ?
[c1 c2] = minimize_expression(2)
function [c1, c2] = minimize_expression(alpha)
fun = @(c) expression_to_minimize(c, alpha);
% Define the initial guess for the optimization
x0 = [0.5, 1];
% Define the lower and upper bounds for the optimization
lb = [0, 0];
ub = [1, Inf];
% Set options for fmincon
options = optimoptions('fmincon', 'Display', 'off', 'Algorithm', 'interior-point', ...
'OptimalityTolerance', 1e-12, 'ConstraintTolerance', 1e-12, ...
'StepTolerance', 1e-12, 'MaxFunctionEvaluations', 1e5, ...
'FunctionTolerance', 1e-12, 'MaxIterations', 1e5, ...
'SpecifyObjectiveGradient', false, 'SpecifyConstraintGradient', false, ...
'HonorBounds', true, 'SubproblemAlgorithm', 'cg', 'CheckGradients', false, ...
'Diagnostics', 'off');%, 'FiniteDifferenceStepSize', [], 'TypicalX', []);
[c, fval] = fmincon(fun, x0, [], [], [], [], lb, ub, [], options);
x = linspace(0, 50, 1001);
f1 = c(1)/c(2) * integral(@(t) t.^(alpha-1)./cosh(t).*(x.^2.*cos(x))./(x.^2+t.^2), 0, Inf,'ArrayValued',1) ...
+ (1-c(1))/c(2) * integral(@(t) t.^alpha./sinh(t).*(x.*sin(x))./(x.^2+t.^2), 0, Inf,'ArrayValued',1);
f2 = sin(x);
plot(x,[f1; f2])
% Return the values of c1 and c2
c1 = c(1);
c2 = c(2);
end
function val = expression_to_minimize(c, alpha)
% Define the function whose infinity norm we want to minimize
x = linspace(0, 50, 1001);
f = c(1) * integral(@(t) t.^(alpha-1)./cosh(t).*(x.^2.*cos(x))./(x.^2+t.^2), 0, Inf,'ArrayValued',1) ...
+ (1-c(1)) * integral(@(t) t.^alpha./sinh(t).*(x.*sin(x))./(x.^2+t.^2), 0, Inf,'ArrayValued',1) - c(2) * sin(x);
val = norm(f, Inf);
end
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