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Results tagged with convex-optimization
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user 91764
Optimization with convex constraints and convex objectives; notions related to convex optimization such as sub-gradients, normal cones, separating hyperplanes
1
vote
Using iterative projection to solve a minimization problem
Given matrices $\mathrm X_0, \mathrm C \in \mathbb R^{n \times n}$,
$$\begin{array}{ll} \text{minimize} & \| \mathrm X - \mathrm X_0 \|_{\text{F}}^2\\ \text{subject to} & \mathrm X 1_n = 1_n\\ & 1_n^ …
1
vote
Algorithm for a linear optimization problem
We have the following linear program (LP) in $\mathrm P \in \mathbb R^{n \times n}$
$$\begin{array}{ll} \text{maximize} & \langle \mathrm C, \mathrm P \rangle\\ \text{subject to} & \mathrm P 1_n = \m …
2
votes
Standard solution to semidefinite program
$$\begin{array}{ll} \text{minimize} & \| \mathrm X \mathrm a - \mathrm b \|_2 \\ \text{subject to} & \mathrm X \succeq \mathrm O_n\end{array}$$
where $\mathrm a, \mathrm b \in \mathbb R^n \setminus \ …
6
votes
Accepted
Minimization problem involving the inverse of an affine matrix function
Rephrasing slightly, given (symmetric) matrix $\mathrm A \succeq \mathrm O_n$, we have the following minimization problem in (symmetric) matrix $\mathrm X \succeq \mathrm O_n$
$$\begin{array}{ll} \te …
7
votes
Complexity of convex quadratically constrained quadratic programming (QCQP)
Convex quadratically constrained quadratic programming (QCQP) can be reduced to semidefinite programming (SDP). Suppose that we are given the following convex QCQP in $\mathrm x \in \mathbb R^n$
$$\be …
0
votes
Iterative matrix inversion with $L^\infty$ norm
Complementing Suvrit's answer, from chapter 6 of Boyd & Vandenberghe:
7
votes
Accepted
Finding Toeplitz matrix nearest to a given matrix
The set of $n \times n$ symmetric Toeplitz matrices is
$$\left\{ x_1 \mathrm M_1 + x_2 \mathrm M_2 + \cdots + x_n \mathrm M_n \mid x_1, x_2, \dots, x_n \in \mathbb R \right\}$$
where $\mathrm M_1, \m …