For questions about conic programming, a generalization of linear and semidefinite programming that considers constraints defined over convex cones.
Questions tagged [conic-programming]
8 questions
5
votes
2 answers
Convex optimization problem not expressible as a conic program
I've been reading Boyd & Vandenberghe and it says that conic programming is a subclass of convex optimization. I haven't been able to find an example of a convex optimization problem that I cannot translate to an equivalent conic optimization…
IOS_DEV
- 541
4
votes
2 answers
How to get 5 points of an ellipse which is internaly tangent to two congruent intersecting circles.
Let two circles $C$ and $C’$ intersecting at points $A$, $B$. I would like to construct an ellipse passing through $A$ and $B$ using the $5$ points construction of GeoGebra (foci unknown). The problem is that the ellipse must have two points of…
3809525720
- 407
3
votes
2 answers
How to derive the dual of a conic programming problem, $\min_{x\in L}\{c^T x: \,\, Ax-b\in K\}$?
I'm trying to get a better understanding of the derivation of the dual problem associated with a given conic problem.
From these notes (pdf alert), a conic problem is written (see page 5) as
$$\min_x \{c^T x: \,\, Ax-b\in K\},\tag1$$
for some…
glS
- 7,963
1
vote
1 answer
Simple examples of conic programming and second order cone programming
I was looking at the book LECTURES ON MODERN CONVEX OPTIMIZATION, by Ben-Tal and Nemirovski, which covers a lot of material on conic optimization or conic programming. The ideas I seem to get, but I am having a hard time understanding the practical…
krishnab
- 2,653
1
vote
1 answer
HARA utility as a power cone
I'm trying to follow the derivation in the following Mosek link where a HARA utility optimization problem is reformulated using power cones (see the secion titled "HARA utility as a Power cone"). We want to maximize the HARA utility function over…
AUK1939
- 385
1
vote
0 answers
Simple representation of a positive linear transformation of a semidefinite cone
I am trying to solve a conic optimization problem where one of my length $n$ vector decision variables is the sum of all of the $n$ unique diagonal bands of any $n \times n$ semidefinite matrix. I can represent this as a linear equality constraint…
0
votes
0 answers
Write an inequality form SDP as an conic form problem in inequality form
I understand that semidefinite programming (SDP) is a subset of conic programming (CP). According to Boyd's Convex Optimization book section 4.6.1, the conic problem in inequality form is written as
$$
\begin{array}{ll}
\text{minimize} & c^Tx…
Nick
- 9
0
votes
1 answer
How is the dual problem for conic programs derived via Lagrangians?
I'm trying to get a better grip of conic programming and the relations between primal and dual problems.
Given a convex problem in standard form, e.g. $\min_x f(x)$ subject to $f_i(x)\le0$, one standard approach (discussed e.g. in these pdf notes)…
glS
- 7,963