Mathematics

Questions tagged [conic-programming]

For questions about conic programming, a generalization of linear and semidefinite programming that considers constraints defined over convex cones.

10 questions
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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
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4
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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
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3
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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
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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
  • 2,705
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
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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…
Nick Engelking
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Understanding the convergence of SDP facial reduction algorithms

From what I understand: When semidefinite programs (SDPs) don't obey Slater conditions, it is not guaranteed that interior-point methods (IPMs) converge. It appears that facial reduction (FR) algorithms resolve this by re-writing such SDPs into…
Kvothe
  • 233
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How to reformulate the log function as its equivalent conic programming?

I am trying to solve an optimization problem that contains power functions. I reformulated the problem via a logarithmic function, and it works well. The terms of the problem involved are similar to $\log(x) = y$ where $(x, y) \in \mathbb{R}$ . Now,…
A.Omidi
  • 177
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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
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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
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