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1# ------------------------------------------------------------------------------ 

2# Copyright (C) 2018-2019 Maximilian Stahlberg 

3# 

4# This file is part of PICOS. 

5# 

6# PICOS is free software: you can redistribute it and/or modify it under the 

7# terms of the GNU General Public License as published by the Free Software 

8# Foundation, either version 3 of the License, or (at your option) any later 

9# version. 

10# 

11# PICOS is distributed in the hope that it will be useful, but WITHOUT ANY 

12# WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR 

13# A PARTICULAR PURPOSE. See the GNU General Public License for more details. 

14# 

15# You should have received a copy of the GNU General Public License along with 

16# this program. If not, see <http://www.gnu.org/licenses/>. 

17# ------------------------------------------------------------------------------ 

18 

19"""Implementation of :class:`LogSumExpConstraint`.""" 

20 

21from collections import namedtuple 

22 

23from .. import glyphs 

24from ..apidoc import api_end, api_start 

25from ..caching import cached_property 

26from .constraint import Constraint, ConstraintConversion 

27 

28_API_START = api_start(globals()) 

29# ------------------------------- 

30 

31 

32class LogSumExpConstraint(Constraint): 

33 """Upper bound on a logarithm of a sum of exponentials.""" 

34 

35 class ExpConeConversion(ConstraintConversion): 

36 """Bound on a log-sum-exp to exponential cone constraint conversion.""" 

37 

38 @classmethod 

39 def predict(cls, subtype, options): 

40 """Implement :meth:`~.constraint.ConstraintConversion.predict`.""" 

41 from ..expressions import RealVariable 

42 from . import AffineConstraint, ExpConeConstraint 

43 

44 n = subtype.argdim 

45 

46 yield ("var", RealVariable.make_var_type(dim=n, bnd=0), 1) 

47 yield ("con", AffineConstraint.make_type(dim=1, eq=False), 1) 

48 yield ("con", ExpConeConstraint.make_type(), n) 

49 

50 @classmethod 

51 def convert(cls, con, options): 

52 """Implement :meth:`~.constraint.ConstraintConversion.convert`.""" 

53 from ..expressions import ExponentialCone 

54 from ..modeling import Problem 

55 

56 x = con.lse.x 

57 n = con.lse.n 

58 b = con.ub 

59 

60 P = Problem() 

61 

62 u = P.add_variable("__u", n) 

63 P.add_constraint((u | 1) <= 1) 

64 

65 for i in range(n): 

66 P.add_constraint((u[i] // 1 // (x[i] - b)) << ExponentialCone()) 

67 

68 return P 

69 

70 @classmethod 

71 def dual(cls, auxVarPrimals, auxConDuals, options): 

72 """Implement :meth:`~.constraint.ConstraintConversion.dual`.""" 

73 # TODO: Verify that this is the dual. 

74 return auxConDuals[0] 

75 

76 def __init__(self, lse, upperBound): 

77 """Construct a :class:`LogSumExpConstraint`. 

78 

79 :param ~picos.expressions.LogSumExp lse: 

80 Constrained expression. 

81 :param ~picos.expressions.AffineExpression upperBound: 

82 Upper bound on the expression. 

83 """ 

84 from ..expressions import AffineExpression, LogSumExp 

85 

86 assert isinstance(lse, LogSumExp) 

87 assert isinstance(upperBound, AffineExpression) 

88 assert len(upperBound) == 1 

89 

90 self.lse = lse 

91 self.ub = upperBound 

92 

93 super(LogSumExpConstraint, self).__init__( 

94 lse._typeStr if isinstance(lse, LogSumExp) else "LSE") 

95 

96 @property 

97 def exponents(self): 

98 """The affine exponents of the bounded log-sum-exp expression.""" 

99 return self.lse.x 

100 

101 @cached_property 

102 def le0(self): 

103 """The :class:`~.exp_logsumexp.LogSumExp` posed to be at most zero.""" 

104 from ..expressions import LogSumExp 

105 

106 if self.ub.is0: 

107 return self.lse 

108 else: 

109 return LogSumExp(self.lse.x - self.ub) 

110 

111 Subtype = namedtuple("Subtype", ("argdim",)) 

112 

113 def _subtype(self): 

114 return self.Subtype(self.lse.n) 

115 

116 @classmethod 

117 def _cost(cls, subtype): 

118 return subtype.argdim + 1 

119 

120 def _expression_names(self): 

121 yield "lse" 

122 yield "ub" 

123 

124 def _str(self): 

125 return glyphs.le(self.lse.string, self.ub.string) 

126 

127 def _get_size(self): 

128 return (1, 1) 

129 

130 def _get_slack(self): 

131 return self.ub.safe_value - self.lse.safe_value 

132 

133 

134# -------------------------------------- 

135__all__ = api_end(_API_START, globals())