1 /* $Id$
2  *
3  * Name:    conv-exprLog.cpp
4  * Author:  Pietro Belotti
5  * Purpose: convexification and bounding methods for the logarithm operator
6  *
7  * (C) Carnegie-Mellon University, 2006-09.
8  * This file is licensed under the Eclipse Public License (EPL)
9  */
10 
11 #include "CouenneCutGenerator.hpp"
12 
13 #include "CouenneTypes.hpp"
14 #include "CouenneExprLog.hpp"
15 #include "CouenneExprPow.hpp"
16 #include "CouenneExprAux.hpp"
17 
18 #include "CouenneProblem.hpp"
19 
20 using namespace Couenne;
21 
22 #define LOG_STEP 10
23 #define LOG_MININF 1e-50
24 
25 // generate convexification cut for constraint w = this
26 
generateCuts(expression * aux,OsiCuts & cs,const CouenneCutGenerator * cg,t_chg_bounds * chg,int wind,CouNumber lbw,CouNumber ubw)27 void exprLog::generateCuts (expression *aux, //const OsiSolverInterface &si,
28 			    OsiCuts &cs, const CouenneCutGenerator *cg,
29 			    t_chg_bounds *chg, int wind,
30 			    CouNumber lbw, CouNumber ubw) {
31   int
32     w_ind = aux       -> Index (), //   dependent variable's index
33     x_ind = argument_ -> Index (); // independent variable's index
34 
35   bool changed =
36     !chg || (cg -> isFirst ()) ||
37     (chg [x_ind].lower() != t_chg_bounds::UNCHANGED) ||
38     (chg [x_ind].upper() != t_chg_bounds::UNCHANGED);
39 
40   CouNumber l, u;
41   argument_ -> getBounds (l, u);
42 
43   enum auxSign sign = cg -> Problem () -> Var (w_ind) -> sign ();
44 
45   // if bounds are very close, convexify with a single line
46   if ((fabs (u - l) < COUENNE_EPS) && (l > COUENNE_EPS)) {
47 
48     CouNumber x0 = 0.5 * (u+l);
49     if (changed) cg -> createCut (cs, log (x0) - 1, sign, w_ind, 1., x_ind, - 1/x0);
50     return;
51   }
52 
53   // fix lower bound
54   if (l < LOG_MININF) l = LOG_MININF;
55   else   // lower segment (if l is far from zero and u finite)
56     if ((u < COUENNE_INFINITY) && changed && sign != expression::AUX_LEQ) {
57 
58       CouNumber dx   = u-l;
59       CouNumber logu = log (u);
60       CouNumber dw   = logu - log (l);
61 
62       cg -> createCut (cs, dx*logu - u*dw, +1, w_ind, dx, x_ind, -dw);
63     }
64 
65   // no need to continue if auxiliary is defined as w >= log (x)
66   if (sign == expression::AUX_GEQ)
67     return;
68 
69   // pick tangent point closest to current point (x0,y0)
70   CouNumber x = (cg -> isFirst ()) ?
71                  1 : powNewton ((*argument_) (), (*aux) (), log, inv, oppInvSqr);
72 
73   // check if outside interval
74   if      (x < l) x = l;
75   else if (x > u) x = u;
76 
77   // fix bound interval (unless you like infinite coefficients)
78   if (u > 1e5 * log (COUENNE_INFINITY) - 1)
79     u = x + (LOG_STEP << cg -> nSamples ());
80 
81   // add upper envelope
82   cg -> addEnvelope (cs, -1, log, inv, w_ind, x_ind, x, l, u, chg, true);
83 }
84