C Interface

2021-09-21T00:00:00+00:00

C quick start

The below solves the problem $\min. x_1, \textrm{subject to } x_3 = 1, x_1 \ge \sqrt{x_2^2 + x_3^2}$. This obviously has the optimal solution $x= (1, 0, 1)^T$.

First we include the headers we need.

#include "wolf.h"
#include <stdio.h>

Then we define the function to output the solver progress during the solution process:

static int print_progress(integer iteration, double *dnfo)
{
	/* Output progress update. */
	printf("%3i %8.1e %8.1e %8.1e %8.1e %11.4e %11.4e %7.3f %8.1e %8.1e %7.1f\n", (int)iteration, dnfo[0], dnfo[1], dnfo[2], dnfo[3], dnfo[4], dnfo[5], dnfo[6], dnfo[7], dnfo[8], dnfo[9]);
	return 0;
}

Inside our main function we declare the problem struct and specify the number of primitive cones for each cone type:

int main()
{
	/* Set up problem struct. */
	wolf_cos_t prob;
	prob.m = 1;
	prob.n = 3;
	prob.nF = 0;
	prob.nL = 0;
	prob.nQ = 1;
	prob.nR = 0;
	prob.nS = 0;
	prob.nP = 0;
	prob.nE = 0;

The actual problem is defined here, with $A=[0 0 1]$, $b=[1]$ and $c=[1 0 0]^T$, and the pointer structure for the second-order cone of size 3.

	integer pQ[2] = { 0, 3 };
	integer pA[4] = { 0, 0, 0, 1 };
	integer iA[1] = { 0 };
	double xA[1] = { 1.0 };
	double b[1] = { 1.0 };
	double c[3] = { 1.0, 0.0, 0.0 };

The unknown variables being optimized, $x$, $y$ and $s$ for the primal and dual problems are declared.

	double x[3], y[1], s[3];

Pointers to all of these arrays are then needed in the problem structure being passed to the solver.

	prob.x = x;
	prob.y = y;
	prob.s = s;

	prob.pQ = pQ;
	prob.pA = pA;
	prob.iA = iA;
	prob.xA = xA;
	prob.b = b;
	prob.c = c;

Set the default parameters, modify the maximum number of iterations or other parameters as desired.

	/* Set default parameters. */
	wolf_setpar(&prob);

	/* Modify default parameters. */
	prob.ipar[WOLF_COS_IS_MAXITER] = 99;

In preparation for calling the solver, we output a header for the callback function output.

	/* Output progress header. */
	printf("\nWolf Conic Optimization Solver\n");
	printf(" It    pinf     dinf     ginf      u       pobj        dobj      alpha    tau     kappa     time\n");
	printf("-------------------------------------------------------------------------------------------------\n");

We now call the solver and check for error messages upon return, displaying the error message if necessary.

	/* Solve the problem. */
	wolf_cos(&prob, print_progress);

	/* Check for error and display message. */
	if (prob.error != 0)
		printf("*** %s ***\n", wolf_geterrormsg(prob.error));

We can then display various solution information details, as required. Here we select a relevant subset for the problem at hand.

	printf("\nSolution info:\n--------------\n");
	printf("Average objective:      %9.7f\n", 0.5*(prob.dnfo[0] + prob.dnfo[1]));
	printf("Iterations:             %d\n", prob.info[0]);
	printf("Primal infeasibility:  %8.1e\n", prob.dnfo[2]);
	printf("Dual infeasiblity:     %8.1e\n", prob.dnfo[3]);
	printf("Relative duality gap:  %8.1e\n", prob.dnfo[4]);

	printf("x = [ %9.7f %9.7f %9.7f ]\n", x[0], x[1], x[2]);
	printf("y = [ %9.7f ]\n", y[0]);
	printf("s = [ %9.7f %9.7f %9.7f ]\n", s[0], s[1], s[2]);

	printf("Second-order cones:    %10li\n", prob.info[5]);
	printf("Non-zeros in A:        %10li (originally %10li)\n", prob.info[7], prob.pA[prob.n]);
	printf("Non-zeros in M:        %10li\n", prob.info[8]);
	printf("Non-zeros in L:        %10li\n", prob.info[9]);
}

This gives the following output before and during the solver’s progress.

Wolf Conic Optimization Solver

 It    pinf     dinf     ginf      u       pobj        dobj      alpha    tau     kappa     time
-------------------------------------------------------------------------------------------------
1.0e+00  4.1e-01  2.4e+00  1.0e+00  1.4142e+00  0.0000e+00   0.000  1.0e+00  1.0e+00     0.0
1.7e-01  6.9e-02  4.0e-01  1.7e-01  1.1089e+00  9.0709e-01   0.841  7.9e-01  2.4e-01     0.0
1.7e-02  7.1e-03  4.1e-02  1.7e-02  1.0115e+00  9.9023e-01   0.900  7.8e-01  2.5e-02     0.0
1.7e-03  7.1e-04  4.2e-03  1.7e-03  1.0012e+00  9.9901e-01   0.900  7.8e-01  2.5e-03     0.0
1.7e-04  7.2e-05  4.2e-04  1.7e-04  1.0001e+00  9.9990e-01   0.900  7.8e-01  2.5e-04     0.0
1.8e-05  7.3e-06  4.2e-05  1.7e-05  1.0000e+00  9.9999e-01   0.900  7.8e-01  2.5e-05     0.0
1.8e-06  7.3e-07  4.3e-06  1.8e-06  1.0000e+00  1.0000e+00   0.900  7.8e-01  2.6e-06     0.0
1.8e-07  7.4e-08  4.3e-07  1.8e-07  1.0000e+00  1.0000e+00   0.900  7.8e-01  2.6e-07     0.0
1.8e-08  7.5e-09  4.4e-08  1.8e-08  1.0000e+00  1.0000e+00   0.900  7.8e-01  2.6e-08     0.0
5.9e-09  7.5e-10  4.4e-09  2.7e-09  1.0000e+00  1.0000e+00   0.900  7.3e-01  4.2e-09     0.0

The extra information displayed after solving is as follows.

Solution info:
--------------
Average objective:      1.0000000
Iterations:             9
Primal infeasibility:   8.1e-09
Dual infeasiblity:      1.0e-09
Relative duality gap:   1.3e-10
x = [ 1.0000000 0.0000000 1.0000000 ]
y = [ 1.0000000 ]
s = [ 1.0000000 0.0000000 -1.0000000 ]

Problem size:
-------------
Number of constraints:          1 (originally          1)
Number of variables:            3 (originally          3)
Second-order cones:             1
Non-zeros in A:                 1 (originally          1)
Non-zeros in M:                 1
Non-zeros in L:                 1

Overview

2021-09-21T00:00:00+00:00

Introduction

The Wolf Optimization solver is a high-performance implementation of a simplified homogeneous self-dual primal-dual interior-point method that is especially efficient at solving large, sparse conic optimization problems. A brief overview of the capabilities and interfaces is included below.

Conic constraints

The Wolf conic optimization solver currently accepts the following conic constraints:

Linear or non-negative orthant, $x \ge 0$
Second-order cone of size $n$ (also known as the conic quadratic cone and Lorentz cone), $x_1 \ge \sqrt{x_2^2 + … + x_n^2}$
Rotated second-order cone of size $n$ (also known as the rotated conic quadratic cone), $2x_1x_2 \ge x_3^2 + … + x_n^2$ [//] # “- Semidefinite cone of size $n \times n$, $v^TXv \ge 0 \, \forall \, v \in \mathbb{R}^n$ (i.e. the symmetric matrix $X$ is positive semidefinite or, equivalently, does not have negative eigenvalues)”
Power cone, $x_1^\alpha x_2^{1-\alpha} \ge |x_3|, \, x_1,x_2 \ge 0$ [//] # “- Exponential cone, $x_1 \ge x_2 e^{x_3/x_2}$”
Free cone, $x \in \mathbb{R}$. While free variables have conventionally been transformed into the difference between two linear variables, it can be advantageous to try and eliminate the free variables from the problem and thus reducing the size of the problem being solved. Those that are not eliminated can then be dealt with explicitly or transformed into linear variables.

Interfaces

The Wolf solver is compiled from C into a library. The library has been tested using C, C#, and MATLAB. Refer to the User Manual for guidance, or see here to get started quickly in C.

User Manual

2021-09-21T00:00:00+00:00

The user manual

A PDF user manual is available here. While not specifically about the Wolf solver, Chapters 3 and 5 of this thesis does delve into the relative performance benefits of various solver components in the context of large sparse problems from finite element limit analysis.