Name
Abstract | ||
|---|---|---|
Given a self-concordant barrier function for a convex set
, we determine a self-concordant barrier function for the conic hull
of
. As our main result, we derive an “optimal” barrier for
based on the barrier function for
. Important applications of this result include the conic reformulation of a convex problem, and the solution of fractional
programs by interior-point methods. The problem of minimizing a convex-concave fraction over some convex set can be solved
by applying an interior-point method directly to the original nonconvex problem, or by applying an interior-point method to
an equivalent convex reformulation of the original problem. Our main result allows to analyze the second approach showing
that the rate of convergence is of the same order in both cases. |
Year | DOI | Venue |
|---|---|---|
1996 | 10.1007/BF02592197 | Math. Program. |
Keywords | Field | DocType |
interior-point method,self-concordant barrier function,." conic hull of a convex set: self-concordant barrier function,conic hull,fractional programming,convex set,barrier function,rate of convergence,interior point method | Discrete mathematics,Mathematical optimization,Convex set,Regular polygon,Rate of convergence,Conic section,Conic optimization,Convex optimization,Interior point method,Mathematics,Fractional programming | Journal |
Volume | Issue | ISSN |
74 | 3 | 1436-4646 |
Citations | PageRank | References |
4 | 1.05 | 4 |
Authors | ||
3 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Roland W. Freund | 1 | 643 | 154.24 |
| Florian Jarre | 2 | 293 | 36.75 |
| Siegfried Schaible | 3 | 148 | 25.89 |