# Questions tagged [convex-optimization]

Convex Optimization is a special case of mathematical optimization where the feasible region is convex and the objective is to either minimize a convex function or maximize a concave function.

250 questions
Filter by
Sorted by
Tagged with
114 views

### How to formulate a convex expression to minimize the difference between Frobenius norm of a positive semidefinite matrix and a positive value

So what I am trying to do is to minimize the distance between the Frobenius norm of a PSD matrix and a real positive value, which can be formulated as $$\min \left|\|\textbf{P}\|_F - J\right|^2$$ ...
73 views

### How to formulate the convex hull which is a regular polygon on the complex plane

Suppose that I have a convex regular polygon with $k$ vertices on the complex plane, and the first vertex lies on the positive real axis. Is there a neat way to formulate the convex hull with the ...
66 views

### How to determine whether the symmetric stiffness matrix is positive definite or not? Is it related to the problem?

For two-dimensional or three-dimensional elliptic equations, when will the stiffness matrix be asymmetric and positive definite? This affected the solution efficiency so much that I had to choose an ...
59 views

### What 2nd-order optimization algorithms have convergence guarantees for strictly- but not strongly-convex problems?

A function $f$ is strictly convex if $$f((1 - \lambda)x + \lambda y) \le (1 - \lambda)f(x) + \lambda f(y)$$ with equality if and only if $x$ and $y$ are equal. This implies that the second derivative ...
1 vote
40 views

### Name this optimum-within-convex-hull algorithm: State is a convex combination of hull vertices; Nonnegativity ensured by reparameterization

I'm looking for the "official" name(s) for a procedure for optimizing a convex loss function over a convex subset. This seems to be a default/naïve algorithm that folks come up with before ...
1 vote
50 views

### Beyond the LP relaxation of binary least squares

I have a binary quadratic program with a convex objective function, of the form, \begin{align} \text{minimize}\;\;& x^tAx+b^tx\\ \text{subject to}\;\;& x_i\in\{0,1\} \end{align} where $A$ is ...
1 vote