laptimize is a python package to solve separable non convex optimization problem which is based on branch and bound algorithm developed by James E.Falk (1972) of The George Washington University. It has been proven that it can generate global solution for large class of nonlinear programming problems in a finite number of steps. In many practical cases Nonlinear optimization problems are hard to solve and only limited methods are implemented. Many such problems, can be approximated arbitrarily closely by separable problems if all functions are piecewise linear. The laptimize python package will find a global optimum to these latter problems.
pip install laptimize
laptimize requires Python >= 3.6
NumPy (>= 1.19.2)
Pandas (>= 1.1.3)
PuLP (>= 2.3)
Refer Examples directory for more examples
problem type which laptimize can applies
Separable linear/non-linear convex/non-convex minimization objective function
Minimize:
F0(x1, x2) = 12x1 + 7x2 - x2^2
Subject to separable linear/non-linear convex/non-convex constraint with '<=' inequality
convex polygon
F1(x1, X2) = 2x1 + x2 - 0 <= 0
non convex constraint
F2(x1, X2) = -2x1^4 -x2 +2 <= 0
0 <= x1 <= 2, 0 <= x1 <= 3
Example Code
from laptimize.solver import Solver
example_1 = {'objective': {'x1': lambda x: 12 * x, 'x2': lambda x: 7 * x - x ** 2},
'constraint_1': {'x1': lambda x: -2 * (x ** 4), 'x2': lambda x: -x, 'value': -2},
'constraint_2': {'x1': lambda x: 2 * x, 'x2': lambda x: x, 'value': 3},
'capacity': {'x1': [0, 2], 'x2': [0, 3]}}
solution = Solver(example_1, partition_len=0.5).solve()
print(solution)
Comments, bug reports, patches and suggestions are welcome.
- Comments and suggestions: https://github.com/uichathurika/laptimize/discussions
- Bug reports: https://github.com/uichathurika/laptimize/issues
- Patches: https://github.com/uichathurika/laptimize/pulls