void better_start(void) {
/* Calculates a better starting point, using a similar approach to CVXOPT. */
/* Not yet speed optimized. */
int i;
double *x, *s, *z, *y;
double alpha;
work.block_33[0] = -1;
/* Make sure sinvz is 1 to make hijacked KKT system ok. */
for (i = 0; i < 84; i++)
work.s_inv_z[i] = 1;
fill_KKT();
ldl_factor();
fillrhs_start();
/* Borrow work.lhs_aff for the solution. */
ldl_solve(work.rhs, work.lhs_aff);
/* Don't do any refinement for now. Precision doesn't matter too much. */
x = work.lhs_aff;
s = work.lhs_aff + 114;
z = work.lhs_aff + 198;
y = work.lhs_aff + 282;
/* Just set x and y as is. */
for (i = 0; i < 114; i++)
work.x[i] = x[i];
for (i = 0; i < 12; i++)
work.y[i] = y[i];
/* Now complete the initialization. Start with s. */
/* Must have alpha > max(z). */
alpha = -1e99;
for (i = 0; i < 84; i++)
if (alpha < z[i])
alpha = z[i];
if (alpha < 0) {
for (i = 0; i < 84; i++)
work.s[i] = -z[i];
} else {
alpha += 1;
for (i = 0; i < 84; i++)
work.s[i] = -z[i] + alpha;
}
/* Now initialize z. */
/* Now must have alpha > max(-z). */
alpha = -1e99;
for (i = 0; i < 84; i++)
if (alpha < -z[i])
alpha = -z[i];
if (alpha < 0) {
for (i = 0; i < 84; i++)
work.z[i] = z[i];
} else {
alpha += 1;
for (i = 0; i < 84; i++)
work.z[i] = z[i] + alpha;
}
}
void refine(double *target, double *var) {
int i, j;
double *residual = work.buffer;
double norm2;
double *new_var = work.buffer2;
for (j = 0; j < settings.refine_steps; j++) {
norm2 = 0;
matrix_multiply(residual, var);
for (i = 0; i < 179; i++) {
residual[i] = residual[i] - target[i];
norm2 += residual[i]*residual[i];
}
#ifndef ZERO_LIBRARY_MODE
if (settings.verbose_refinement) {
if (j == 0)
printf("Initial residual before refinement has norm squared %.6g.\n", norm2);
else
printf("After refinement we get squared norm %.6g.\n", norm2);
}
#endif
/* Solve to find new_var = KKT \ (target - A*var). */
ldl_solve(residual, new_var);
/* Update var += new_var, or var += KKT \ (target - A*var). */
for (i = 0; i < 179; i++) {
var[i] -= new_var[i];
}
}
#ifndef ZERO_LIBRARY_MODE
if (settings.verbose_refinement) {
/* Check the residual once more, but only if we're reporting it, since */
/* it's expensive. */
norm2 = 0;
matrix_multiply(residual, var);
for (i = 0; i < 179; i++) {
residual[i] = residual[i] - target[i];
norm2 += residual[i]*residual[i];
}
if (j == 0)
printf("Initial residual before refinement has norm squared %.6g.\n", norm2);
else
printf("After refinement we get squared norm %.6g.\n", norm2);
}
#endif
}
long solve(void) {
int i;
int iter;
double *dx, *ds, *dy, *dz;
double minval;
double alpha;
work.converged = 0;
setup_pointers();
pre_ops();
#ifndef ZERO_LIBRARY_MODE
if (settings.verbose)
printf("iter objv gap |Ax-b| |Gx+s-h| step\n");
#endif
fillq();
fillh();
fillb();
if (settings.better_start)
better_start();
else
set_start();
for (iter = 0; iter < settings.max_iters; iter++) {
for (i = 0; i < 84; i++) {
work.s_inv[i] = 1.0 / work.s[i];
work.s_inv_z[i] = work.s_inv[i]*work.z[i];
}
work.block_33[0] = 0;
fill_KKT();
ldl_factor();
/* Affine scaling directions. */
fillrhs_aff();
ldl_solve(work.rhs, work.lhs_aff);
refine(work.rhs, work.lhs_aff);
/* Centering plus corrector directions. */
fillrhs_cc();
ldl_solve(work.rhs, work.lhs_cc);
refine(work.rhs, work.lhs_cc);
/* Add the two together and store in aff. */
for (i = 0; i < 294; i++)
work.lhs_aff[i] += work.lhs_cc[i];
/* Rename aff to reflect its new meaning. */
dx = work.lhs_aff;
ds = work.lhs_aff + 114;
dz = work.lhs_aff + 198;
dy = work.lhs_aff + 282;
/* Find min(min(ds./s), min(dz./z)). */
minval = 0;
for (i = 0; i < 84; i++)
if (ds[i] < minval*work.s[i])
minval = ds[i]/work.s[i];
for (i = 0; i < 84; i++)
if (dz[i] < minval*work.z[i])
minval = dz[i]/work.z[i];
/* Find alpha. */
if (-0.99 < minval)
alpha = 1;
else
alpha = -0.99/minval;
/* Update the primal and dual variables. */
for (i = 0; i < 114; i++)
work.x[i] += alpha*dx[i];
for (i = 0; i < 84; i++)
work.s[i] += alpha*ds[i];
for (i = 0; i < 84; i++)
work.z[i] += alpha*dz[i];
for (i = 0; i < 12; i++)
work.y[i] += alpha*dy[i];
work.gap = eval_gap();
work.eq_resid_squared = calc_eq_resid_squared();
work.ineq_resid_squared = calc_ineq_resid_squared();
#ifndef ZERO_LIBRARY_MODE
if (settings.verbose) {
work.optval = eval_objv();
printf("%3d %10.3e %9.2e %9.2e %9.2e % 6.4f\n",
iter+1, work.optval, work.gap, sqrt(work.eq_resid_squared),
sqrt(work.ineq_resid_squared), alpha);
}
#endif
/* Test termination conditions. Requires optimality, and satisfied */
/* constraints. */
if ( (work.gap < settings.eps)
&& (work.eq_resid_squared <= settings.resid_tol*settings.resid_tol)
&& (work.ineq_resid_squared <= settings.resid_tol*settings.resid_tol)
) {
work.converged = 1;
work.optval = eval_objv();
return iter+1;
}
}
return iter;
}
