# 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.

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### trust region method for linearly-constrained convex optimization

I'm interested in the problem of minimizing a convex function $f(x)$ for $x$ living in some Banach space $X$, subject to the linear constraint $Kx = g$ where $K : X \to Y^*$ for some other space $Y$. ...
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### Why using large bound to supplement inifinity in interior point method can be bad

Here in the documentation of mosek (https://docs.mosek.com/latest/pythonfusion/debugging-numerical.html) we see: Never use a very large number as replacement for infinity . Instead define the ...
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### 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 $$\min \left|\|\textbf{P}\|_F - J\right|^2$$ ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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### min(f(x)) is convex or concave based on type of f(x)

i have f(x) that is concave function. My question is g=min(f(x)) is concave or convex? And max(g) is concave or convex? there is a theorem for this?
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### Help with CVXPY and Disciplined Convex Programming

I'm trying to recreate Figure 1 in this paper. This requires maximizing equation (19), which I have convinced myself is concave, but I am having trouble implementing it in CVXPY. Here is the code I ...
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### Problem in parameterizing a CVXPY program

I am trying to parameterize a CVXPY program as I need to repeatedly solve the problem, but I noticed that when my parameters are complex numbers, CVXPY models the problem in each iteration. For ...
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### What is this QR-factorization-based preconditioning called?

I have recently started to delve into someone else's code, and there is a part in there I don't quite understand. The authors of the code use some form of pre-conditioning to speed up the optimization....
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