compute cost reducing path in an euclidian space in matlab

To compute the cost-reducing path in an Euclidean space, you can use optimization algorithms in MATLAB such as fmincon.

Here is an example code that computes the cost-reducing path between two points (start and end) in a 2D Euclidean space:

main.m
% Define start and end points
start = [0,0];
end_point = [10,10];

% Define cost function
cost_fun = @(x) norm(x-start) + norm(x-end_point);

% Define initial guess
x0 = [5,5];

% Define bounds
lb = [0,0];
ub = [10,10];

% Use fmincon algorithm to compute the cost-reducing path
options = optimoptions('fmincon','Display','iter');
[x,fval] = fmincon(cost_fun,x0,[],[],[],[],lb,ub,[],options);
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In this example, the cost function is defined as the sum of distances between the current point and the start point, and the current point and the end point. The fmincon algorithm is used to find the point that minimizes this cost function. The lb and ub variables define the lower and upper bounds for the optimization algorithm, respectively.

After running this code, the optimal point (x) and the minimum cost (fval) will be returned.