text: /***********************************************************************/
  /*                                                                     */
  /*   svm_loqo.c                                                        */
  /*                                                                     */
  /*   Interface to the PR_LOQO optimization package for SVM.            */
  /*                                                                     */
  /*   Author: Thorsten Joachims                                         */
  /*   Date: 19.07.99                                                    */
  /*                                                                     */
  /*   Copyright (c) 1999  Universitaet Dortmund - All rights reserved   */
  /*                                                                     */
  /*   This software is available for non-commercial use only. It must   */
  /*   not be modified and distributed without prior permission of the   */
  /*   author. The author is not responsible for implications from the   */
  /*   use of this software.                                             */
  /*                                                                     */
  /***********************************************************************/
  
  # include <math.h>
  # include "pr_loqo/pr_loqo.h"
  # include "svm_common.h"
  
  /* Common Block Declarations */
  
  long verbosity;
  
  /* /////////////////////////////////////////////////////////////// */
  
  # define DEF_PRECISION_LINEAR    1E-8
  # define DEF_PRECISION_NONLINEAR 1E-14
  
  double *optimize_qp();
  double *primal=0,*dual=0;
  double init_margin=0.15;
  long   init_iter=500,precision_violations=0;
  double model_b;
  double opt_precision=DEF_PRECISION_LINEAR;
  
  /* /////////////////////////////////////////////////////////////// */
  
  void *my_malloc();
  
  double *optimize_qp(qp,epsilon_crit,nx,threshold,learn_parm)
  QP *qp;
  double *epsilon_crit;
  long nx; /* Maximum number of variables in QP */
  double *threshold;
  LEARN_PARM *learn_parm;
  /* start the optimizer and return the optimal values */
  {
    register long i,j,result;
    double margin,obj_before,obj_after;
    double sigdig,dist,epsilon_loqo;
    int iter;
   
    if(!primal) { /* allocate memory at first call */
      primal=(double *)my_malloc(sizeof(double)*nx*3);
      dual=(double *)my_malloc(sizeof(double)*(nx*2+1));
    }
    
    if(verbosity>=4) { /* really verbose */
      printf("\n\n");
      for(i=0;i<qp->opt_n;i++) {
        printf("%f: ",qp->opt_g0[i]);
        for(j=0;j<qp->opt_n;j++) {
  	printf("%f ",qp->opt_g[i*qp->opt_n+j]);
        }
        printf(": a=%.30f",qp->opt_xinit[i]);
        printf(": y=%f\n",qp->opt_ce[i]);
      }
      printf("\n");
    }
  
    obj_before=0; /* calculate objective before optimization */
    for(i=0;i<qp->opt_n;i++) {
      obj_before+=(qp->opt_g0[i]*qp->opt_xinit[i]);
      obj_before+=(0.5*qp->opt_xinit[i]*qp->opt_xinit[i]*qp->opt_g[i*qp->opt_n+i]);
      for(j=0;j<i;j++) {
        obj_before+=(qp->opt_xinit[j]*qp->opt_xinit[i]*qp->opt_g[j*qp->opt_n+i]);
      }
    }
  
    result=STILL_RUNNING;
    qp->opt_ce0[0]*=(-1.0);
    /* Run pr_loqo. If a run fails, try again with parameters which lead */
    /* to a slower, but more robust setting. */
    for(margin=init_margin,iter=init_iter;
        (margin<=0.9999999) && (result!=OPTIMAL_SOLUTION);) {
      sigdig=-log10(opt_precision);
  
      result=pr_loqo((int)qp->opt_n,(int)qp->opt_m,
  		   (double *)qp->opt_g0,(double *)qp->opt_g,
  		   (double *)qp->opt_ce,(double *)qp->opt_ce0,
  		   (double *)qp->opt_low,(double *)qp->opt_up,
  		   (double *)primal,(double *)dual, 
  		   (int)(verbosity-2),
  		   (double)sigdig,(int)iter, 
  		   (double)margin,(double)(qp->opt_up[0])/4.0,(int)0);
  
      if(isnan(dual[0])) {     /* check for choldc problem */
        if(verbosity>=2) {
  	printf("NOTICE: Restarting PR_LOQO with more conservative parameters.\n");
        }
        if(init_margin<0.80) { /* become more conservative in general */
  	init_margin=(4.0*margin+1.0)/5.0;
        }
        margin=(margin+1.0)/2.0;
        (opt_precision)*=10.0;   /* reduce precision */
        if(verbosity>=2) {
  	printf("NOTICE: Reducing precision of PR_LOQO.\n");
        }
      }
      else if(result!=OPTIMAL_SOLUTION) {
        iter+=2000; 
        init_iter+=10;
        (opt_precision)*=10.0;   /* reduce precision */
        if(verbosity>=2) {
  	printf("NOTICE: Reducing precision of PR_LOQO.\n");
        }      
      }
    }
  
    if(qp->opt_m)         /* Thanks to Alex Smola for this hint */
      model_b=dual[0];
    else
      model_b=0;
  
    /* Check the precision of the alphas. If results of current optimization */
    /* violate KT-Conditions, relax the epsilon on the bounds on alphas. */
    epsilon_loqo=1E-10;
    for(i=0;i<qp->opt_n;i++) {
      dist=-model_b*qp->opt_ce[i]; 
      dist+=(qp->opt_g0[i]+1.0);
      for(j=0;j<i;j++) {
        dist+=(primal[j]*qp->opt_g[j*qp->opt_n+i]);
      }
      for(j=i;j<qp->opt_n;j++) {
        dist+=(primal[j]*qp->opt_g[i*qp->opt_n+j]);
      }
      /*  printf("LOQO: a[%d]=%f, dist=%f, b=%f\n",i,primal[i],dist,dual[0]); */
      if((primal[i]<(qp->opt_up[i]-epsilon_loqo)) && (dist < (1.0-(*epsilon_crit)))) {
        epsilon_loqo=(qp->opt_up[i]-primal[i])*2.0;
      }
      else if((primal[i]>(0+epsilon_loqo)) && (dist > (1.0+(*epsilon_crit)))) {
        epsilon_loqo=primal[i]*2.0;
      }
    }
  
    for(i=0;i<qp->opt_n;i++) {  /* clip alphas to bounds */
      if(primal[i]<=(0+epsilon_loqo)) {
        primal[i]=0;
      }
      else if(primal[i]>=(qp->opt_up[i]-epsilon_loqo)) {
        primal[i]=qp->opt_up[i];
      }
    }
  
    obj_after=0;  /* calculate objective after optimization */
    for(i=0;i<qp->opt_n;i++) {
      obj_after+=(qp->opt_g0[i]*primal[i]);
      obj_after+=(0.5*primal[i]*primal[i]*qp->opt_g[i*qp->opt_n+i]);
      for(j=0;j<i;j++) {
        obj_after+=(primal[j]*primal[i]*qp->opt_g[j*qp->opt_n+i]);
      }
    }
  
    /* if optimizer returned NAN values, reset and retry with smaller */
    /* working set. */
    if(isnan(obj_after) || isnan(model_b)) {
      for(i=0;i<qp->opt_n;i++) {
        primal[i]=qp->opt_xinit[i];
      }     
      model_b=0;
      if(learn_parm->svm_maxqpsize>2) {
        learn_parm->svm_maxqpsize--;  /* decrease size of qp-subproblems */
      }
    }
  
    if(obj_after >= obj_before) { /* check whether there was progress */
      (opt_precision)/=100.0;
      precision_violations++;
      if(verbosity>=2) {
        printf("NOTICE: Increasing Precision of PR_LOQO.\n");
      }
    }
  
    if(precision_violations > 50) { 
      (*epsilon_crit)*=10.0;
      if(verbosity>=1) {
        printf("\nWARNING: Relaxing epsilon on KT-Conditions.\n");
      }
    }	  
  
    (*threshold)=model_b;
  
    if(result!=OPTIMAL_SOLUTION) {
      printf("\nERROR: PR_LOQO did not converge. \n");
      return(qp->opt_xinit);
    }
    else {
      return(primal);
    }
  }
  
  