清空筛选条件
清空筛选条件

Supremum of a concave function

3 次查看（过去 30 天）
Waqar Ahmed
Waqar Ahmed 2021-1-1
回答： Walter Roberson 2021-1-2
I have a function I want to calculate its supremum. The function is below.
-0.25* (c+A^t-v)^T *(c+A^t-v)/v for all v>0
  2 个评论
Image Analyst
Image Analyst 2021-1-1
编辑：Image Analyst 2021-1-1
numPoints = 1000;
v = linspace(0.02, 1, 1000);
% Guesses:
c = 1 * ones(1, numPoints);
A = 2 * ones(1, numPoints);
T = 2 * ones(1, numPoints);
t = 3 * ones(1, numPoints);
% Compute function
y = -0.25 * (c+A.^t-v).^T .* (c+A.^t-v)./v %for all v>0
% Plot it.
plot(v, y, 'b.-', 'LineWidth', 2);
grid on;
What are c, A, t, and T?
John D'Errico
John D'Errico 2021-1-1
编辑：John D'Errico 2021-1-1
What do you know about c, A, t, and T? T is most important, of course. For example, if T is not an integer, then things are, let me say, difficult? That is because noninteger powers of negative numbers will be complex, so that supremem will be a nasty thing.

请先登录，再进行评论。

请先登录，再回答此问题。

回答（1 个）

Walter Roberson
Walter Roberson 2021-1-2
Ran in:
This creates a list of supermum for the function, together with the conditions under which the supermum hold. The calculations would have been easier if we had been given more information about the symbols.
syms A t T v c;
f = -0.25* (c+A^t-v)^T *(c+A^t-v)/v;
df = diff(f,v);
sol = solve(df == 0,v,'returnconditions', true);
flavor = simplify(subs(diff(df,v),v,sol.v));
conditional_flavor = arrayfun(@(F,C) simplify(piecewise(C & F>0,symtrue,nan)), flavor, sol.conditions);
bs1 = [T == -1, T==0, T==1, T~=-1 & T~=0 & T~=1 & 1<real(T), T~=-1 & T~=0 & T~=1 & 1>real(T)];
bs2 = [c + A^t~=0, c + A^t==0];
branches = and(bs1, bs2(:));
for bidx = 1 : numel(branches)
assume(assumptions, 'clear')
assume(branches(bidx));
constrained_conditions(:,bidx) = simplify(conditional_flavor);
end
assume(assumptions, 'clear')
supermum= [];
for K = 1: size(constrained_conditions,1)
for bidx = find(~isnan(constrained_conditions(K,:)))
temp = arrayfun(@(C) simplify(piecewise(v == sol.v(K) & C, subs(f, v, sol.v(K)))), branches(bidx) & constrained_conditions(K,bidx));
supermum = [supermum; temp];
end
end
supermum
supermum = 
There is also a saddle point of f = 0 when v = c + A^t

类别

在 Help Center 和 File Exchange 中查找有关 Calculus 的更多信息

标签

Community Treasure Hunt

Find the treasures in MATLAB Central and discover how the community can help you!

Start Hunting!

Translated by