# Questions tagged [constrained-optimization]

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### Efficient preconditioner for Augmented Lagrangian

I want to solve a non-linear problem with non-linear equality constrains and I'm using a augmented Lagrangian with a penalty regularization term that, as well known, spoils the condition number of my ...
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### Why are interior point methods difficult to warm start?

I often encounter the general adage that interior point methods are difficult to warm start. Is there an intuitive explanation behind this advice? Are there situations in which one can expect benefits ...
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### Interpolation by Solving a Minimization Problem (Optimization)

I will try to give the motivation behind this problem and later the math formality. Given a grayscale image (1 Channel - $M \times N$ Matrix). Someone marks some pixels as anchors. Now, you need to ...
152 views

### Maximize a function of an orthogonal matrix

I'm trying to write up a small code that, given a set of normal vibrational modes for a molecule, will convert them to localized vibrational modes. To do this I'm following the procedure from J. Chem. ...
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### How to determine whether two cylinders intersect or not?

Considering any two cylinders, defined as: the center of their bottoms $A_i$, the radius of their bottom $R_i$, the unit vector $W_i$ of their axis direction, and the length $L_i$ of the cylinders, ...
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### Projection on Stiefel manifold after integration step

A few days ago, I asked how constraints like $A^T A = I$ can be implemented if one wishes to integrate differential equations of the form $\dot{A}=f(A,t)$. Kirill was so kind to point out that a ...
134 views

### Can Variational Inequalities handle non-symmetric matrices?

I am trying to enforce the discrete maximum principle (i.e., ensuring non-negative concentrations) for diffusion-type problems that have an anisotropic diffusivity tensor (e.g., tensor dispersion from ...
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### How does fmincon in MATLAB calculate gradients?

I am trying to solve numerically a constrained optimisation problem in MATLAB, and I am wondering how the fmincon function calculates gradients when one isn't ...
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### Best platform for complex SDPs with n and m around 5-15K?

I am looking to solve a class of SDPs with complex entries, with the semi-definite cone $S^n$, $n$ around 5000 to 15000. Also, $m$, the number of equality/inequality constraints is close to $n$. I ...
129 views

### optimization subject to disjunction of inequality constraints

I want to solve $$\min_x f(x)\qquad \textrm{s.t.}\qquad g_i(x) \geq 0\ \ \textrm{or}\ \ h_i(x) \geq 0$$ for $i=1,\ldots,m$. Clearly if the inequality constraints split the feasible set into $2^m$ ...
594 views

### Finding a global minimum of non-convex quasi-smooth function that is costly to evaluate

I have a bounded non-convex function in 10-dimensional space. The function is quasi-smooth, you can imagine a histogram, here is an illustration, it just shows the idea and not related to my ...
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### State-of-the-art for active set optimization algorithms?

Given a problem like this: $$\text{min } ||Ex-f|| \text{ s.t.}$$ $$Gx \ge 0$$ $$Cx = d$$ And assuming that the matrices are medium sized (dimensions in the low thousands) and dense, what's the ...
Given three vectors in $\mathbb{R}^{512}$, my task is to compute a Minimum Volume Enclosing Ellipsoid (MVEE). I have tried Kachiyan's algorithm, but it requires at least as many vectors as there are ...