sqlp: Solve Second Order Cone Programs

In DWD: DWD implementation based on A IPM SOCP solver

Description

solve an SOCP program by infeasible path-following method

Usage

sqlp(blk,At,C,b,OPTIONS,X0,y0,Z0)

Arguments

blk	a list describing the structure of the SOCP data.
At	a matrix containing the coefficients for the linear and second order cone constraints. At should have m columns, where m is the number of constraints. The number of rows in At should be sum(C).
C	a vector containing the coefficients of the objective function to be minimized.
b	a vector containing the right hand side of the constraints.
OPTIONS	a list that specifies parameters required in sqlp.
X0	an initial iterate for primal solution.
y0,Z0	initial iterates for dual solution.

Details

A second order cone program (SOCP) is an optimization problem similar to a linear program (LP), except that some variables can be constrained by second order cones. An exact mathematical definition can be found in Kim-Chuan Toh , Michael J. Todd, and Reha H. Tutuncu. This function implements the algorithm given in that paper which allows for multiple second order cone constraints as well as linear constraints. The objective function is given by sum(C*x) while the constraints are A%*%x == b, with x belonging to the cartesian product of second order cones described by blk.

Value

A list containing named elements:

x	The optimal solution to the SOCP.
y,Z	The dual solutions.
info	Summary information.
runhist	Run history.

Author(s)

Hanwen Huang: [e-mail]; Perry Haaland: [e-mail]; Xiaosun Lu: [e-mail]; Frances Tong: [e-mail]; Elaine McVey: [e-mail]; Yufeng Liu: [e-mail]; J. S. Marron: [e-mail]

References

Kim-Chuan Toh , Michael J. Todd, and Reha H. Tutuncu
SDPT3 version 4.0 – a MATLAB software for semidefinite-quadratic-linear programming
http://www.math.nus.edu.sg/~mattohkc/sdpt3.html

Examples

#Load an example SOCP
data(sqlpData)

#Solve the socp
soln <- sqlp(blk=sqlpData$blk,At=sqlpData$At,C=sqlpData$C,b=sqlpData$b,X0=sqlpData$X0,y0=sqlpData$y0,Z0=sqlpData$Z0)

DWD documentation built on May 2, 2019, 5 p.m.