# Tag Info

### What is required of the objective function in order to use Gauss Newton method?

Just to clarify notation, I'll be discussing the Gauss-Newton method for the problem $\min \phi(x)=(1/2) \| F(x) \|_{2}^{2}$ with the search direction $p$ computed as the solution to the linear ...
• 18.9k
Accepted

### Looking for name of optimization problem in form $\min \mathrm x^T \mathrm A \mathrm x$ subject to $\|\mathrm x\| = 1$

Since the optimization problem has a well-known closed-form solution, it is rarely used in itself and hence usually not given a name. The objective function $x^TAx$ (using $\|x\|=1$), however, is ...
• 12.4k
Accepted

### How do I check if a loss function can achieve its minimum?

TL;DR: The property you are looking for is coercivity. This is satisfied for the example in your question (as are properties 1 and 3 below), and hence yes, the penalized objective attains its minimum. ...
• 12.4k
Accepted

### Can this simple quadratic optimization problem be turned into a simple eigenvalue problem?

At least for the second question the answer is yes. See for example Mattheij, Robert MM, and Gustaf Söderlind. "On inhomogeneous eigenvalue problems. I." Linear Algebra and its Applications ...
• 188

### How to debug a constrained optimization algorithm?

In addition to the things that @Dirk already states, run your algorithm on a problem that is simple enough that you can do each step of the algorithm exactly on a piece of paper. Then compare what ...
• 56.2k

### How to debug a constrained optimization algorithm?

Writing an optimization routine is like writing any other not too simple program and involves a fair amount of debugging. All things you mention in your question are good checks (i.e. taking care that ...
• 1,748

### Looking for name of optimization problem in form $\min \mathrm x^T \mathrm A \mathrm x$ subject to $\|\mathrm x\| = 1$

I know this should be a comment but I do not have enough reputation to comment. I just want to point out that for an arbitrary $A$ with real entries the solution (minimum) to this problem is the ...
• 101
Accepted

Let's consider the following minimization problem \begin{align} & \text{minimize} && \tfrac12 z^\mathrm{H} P_0 z + q_0^\mathrm{H} z\\ & \text{subject to} && \tfrac12 z^\mathrm{...
• 8,582

• 18.9k

### Nature of stationary points of a Lagrangian fuction

By the very definition of the Lagrangian, the extrema of the original, constrained problem are stationary points of the Lagrangian. That's just how the Lagrangian is defined. What you are looking for ...
• 56.2k

Only top scored, non community-wiki answers of a minimum length are eligible