Questions tagged [optimization]
This tag is intended for questions on methods for the (constrained or unconstrained) minimization or maximization of functions.
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formula for the elliptical orbit of the magnetic field in a current carrying circular loop [closed]
In a circular current carrying loop the magnetic field lines form elliptical orbits if I have constant value for current and a point let's say at r distance from the center of th current carrying loop ...
-1
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1
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68
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optimal gradient algorithm to determine best $α_k$
Let's consider an optimal-step gradient algorithm and assume that:
$g(α) := f(X_k - α∇f(X_k)) = 2α^2-4α+17$, how can we determine the optimal $α_k$?
Here is my simple solution:
$g(α) = 2α^2-4α+17$
$g'(...
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step-fixed algorithm first iterates
let us have the fixed-step gradient algorithm, with $p = 2$ and we assume that for $X = (x, y)$,
$∇ f(X) = \begin{pmatrix}
x -1\\
y -2
\end{pmatrix}$
Let me assume we intialize with $X_0 = (0,0)$ what ...
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step-fixed algorithm to minimize f, which step to ensure convergence?
If we want to apply the fixed-step gradient algorithm to the minimization of $f(x) = \frac{1}{2}(Ax, x)$ where $A$ is a symmetric 2x2 matrix with eigenvalues $\lambda_1 > \lambda_2 > 0$, for ...
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Estimating the rate of convergence of Projected Gradient Descent on constrained polynomial objectives
I am estimating the order of convergence of Projected Gradient Descent (GD) on quadratic polynomials with random coefficients independently drawn from Uniform(-1,1) and bounded by a unit hypercube. I'...
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89
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How to run scipy.optimize.minimize with L-BFGS-B for maxiter (completely)
I want to run the below code for maxiter = 20001. I don't want it to stop by some default criteria.
...
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191
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Solving linear system of equations with constraints on unknowns
I would like to solve a system of linear equations $y=Uh$ for an unknown vector $h$, where I have a few constraints on some of the elements of $h$. The matrix $U$ is composed of a vector $u$ (length $...
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LBFGS-B initial gradients too high?
I'm optimizing a geometrical shape for electromagnetic performance. The shape is constrained with bounds, say between 0.2 and 0.8, whereas the parameters are all between 0.2 and 0.8.
I am interested ...
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2
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92
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An alternative to Levenberg–Marquardt algorithm
When trying to solve for a (over)determined non-linear least square method:
$$\underset{x}{\min}||f(x)||^2_2, f: \mathbb{R}^n \rightarrow \mathbb{R}^m, x\in \mathbb{R}^n, m\geq n$$
we use the Gauss-...
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Are penalty functions still "necessary"?
In my constrained problems (box constraints) I simply set my cost function to INFINITY (the c99 macro) if an inequality constraint is violated. This prevents the point being used, seems to work very ...
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132
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Algorithm to find local minima of function which is unbounded from below
I have a differentiable function $\mathbb{R}^n \to \mathbb{R} $ of several variables $f(x_1,\ldots,x_n)$, whose form I can write down and compute derivatives of. Typically $n = 8$.
The function is ...
- 57
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Unable to decipher the error in Anderson-Darling estimation code in R
I just ran the code in R, which estimates some parameters using Anderson-Darling estimation method. The code is given in the appendix of the Habib-Khalil paper.
...
- 111
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Is there existing code for solving a Lagrangian Dual problem using the subgradient method?
I know there is a generic code for solving the lagrangian relaxation of an LP. However, for an integer program, sometimes you want some constraints relaxed, but not all. For example, I want the ...
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How to spot a "centre-bias operator"?
I recently asked this question after noticing abnormally good results from a popular "nature-based meta-heuristic algorithm". I established by "origin shifting" that the method ...
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Ensuring IEEE 754 Compliance and Numerical Precision in C++ HPC Projects
I'm currently engaged in a large-scale C++ HPC project focused on numerical simulation, particularly Finite Element Method (FEM) simulations. Our project spans various Linux-based platforms and ...
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