The SOCP Barrier Solver included free with the Solver
Platform SDK uses Interior Point (Barrier) methods
to solve linear programming (LP), quadratic programming (QP),
quadratically constrained programming (QCP), and second
order cone programming (SOCP) problems of up to 2,000
variables. When given coefficients for quadratic and
conic function Hessians, it is able to solve quadratic and conic problems
with the same speed and reliability as linear programming
problems. It is typically as fast or faster than the
LP/Quadratic Solver included in the Solver Platform SDK.
Below is example code in C# using the SOCP Barrier
Solver to optimize the problem:
Minimize x4 + x5
Subject to x0 + x1 + x2 + x3 = 1
x4,x0,x1 belong to a cone
x5,x2,x3 belong to a cone
using (Problem problem = new
Problem(Solver_Type.Minimize, nvars, ncons))
{
problem.Model.AllLinear[Function_Type.Objective]
=
new
DoubleMatrix(Array_Order.ByRow, 1, nvars, objcoeff);
problem.Model.AllLinear[Function_Type.Constraint]
=
new
DoubleMatrix(Array_Order.ByRow, ncons, nvars, concoeff);
problem.FcnConstraint.LowerBound.Array = rhsvalue;
problem.FcnConstraint.UpperBound.Array = rhsvalue;
problem.VarDecision.NonNegative();
// Specify the second order cone
constraints
problem.VarDecision.ConeType.Array =
new
Cone_Type [] { Cone_Type.SOC, Cone_Type.SOC, Cone_Type.SOC,
Cone_Type.SOC,
Cone_Type.SOC_Start, Cone_Type.SOC_Start };
problem.VarDecision.ConeIndex.Array = new
int [] { 1, 2, 1, 2, 1, 2 };
problem.Engine = problem.Engines[Engine.SOCPName];
problem.Solver.Optimize();
Optimize_Status status = problem.Solver.OptimizeStatus;
m_Log.Dump("Status = " + status);
m_Log.Dump("x1 = " +
problem.VarDecision.FinalValue[0]);
...
}
The SOCP Barrier Solver automatically
recognizes quadratic objectives and constraints and converts
them to second order cone (SOC) constraints internally before
solving the problem. It provides several options for computing the
search direction in each Interior Point iteration, and it allows you
control tolerances such as the feasibility tolerance, the
primal-dual gap tolerance, and the relative step size to the
constraint boundary.
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