denis-bz

lp_np: numpy <--> GLPK, the gnu linear programming kit

Keywords: linear programming, LP, python, numpy, scipy, GLPK, GMPL, translate

lp_np connects the numpy-scipy-python world to the GNU Linear Programming Kit GLPK, to have the advantages of both:

• numpy and scipy help construct large sparse LP models, and connect to dozens of specialized tools
• GLPK reads and writes LP models in many formats.

denis-bz

A 6 x 6 linprog testcase from glpk: 3 methods x sparse / dense give different results

transp-linprog.py below is a 6 x 6 testcase of scipy.optimize.linprog from a GLPK example, transp. In outline:

for method in ["interior-point", "revised simplex", "simplex"]:
    for sparse in [True, False]
        try:
            linprog( ... )

denis-bz

Easy lower-risk stochastic programming: the Dakota problem

Keywords: stochastic programming, risk, linear programming, python

Users of stochastic programming sometimes look only at "expected" payoff and ignore risk. For example, a well-known tutorial problem, Dakota furniture from Higle 2005, gives a max-expected profit $ 1730, but with 30 % chance of $ 650 loss, 70 % $2750 profit. That looks risky to me (an engineer, not a businessman).

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Intergrid: interpolate data given on an N-d rectangular grid
============================================================

Purpose: interpolate data given on an N-dimensional rectangular grid,
uniform or non-uniform,
with the fast `scipy.ndimage.map_coordinates` .
Non-uniform grids are first uniformized with `numpy.interp` .

Background:
the reader should know some Python and NumPy

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# A summary of the problems in glpk-4.65/examples/*.mod
#            lp/mip  min/max  rows  cols  nnz
assign     p lp min 17 64 192
bpp        p mip min 11 28 56
cal        p lp min 0 0 0
cf12a      p lp min 20 40 113
cf12b      p lp min 58 41 152
cflsq      p lp min 40 40 114
color      p mip min 92 48 288
cpp        p lp min 30 14 59

denis-bz

timeit scipy.sparse linear solvers: spsolve qmr lgmres splu spilu

Here is a simple test of 5 scipy.sparse solvers of Ax = b, with A = diag*I + sparse random-uniform 4000 x 4000, density 1e-3.

Keywords: sparse linear solver, test case, random matrix, scipy, GMRES, Krylov

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denis-bz

3-point and 5-point finite-difference derivative approximations

Central differences like

diff1 = (f_{t+1} - f{t-1}) / 2,  [0 -1 0 1 0] / 2
diff2 = (f_{t+2} - f{t-2}) / 4,  [-1 0 0 0 1] / 4

approximate the derivative f'(t) much better then the one-sided difference f_{t+1} - f_t; see e.g. Wikipedia

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ABXC nonsmooth optimization problems

ABXC is a range of nonsmooth optimization problems from Curtis et al.; see the problem description and links in abxc.py below. They're hard to optimize, very noisy near minima, and some are infeasible. Here's a plot of scipy.optimize.trust-constr creeping up an infeasible slope:

denis-bz

Mopta08-py

MOPTA08 is a test case for optimization from D.R. Jones, "Large-scale multi-disciplinary mass optimization in the auto industry" , 2008. It has 124 variables in 0 .. 1, a linear objective function, and 68 nonlinear constraints.

The purpose of mopta08-py is to try out various optimizers -> python -> MOPTA08,

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#!/usr/bin/env python2
""" coord_sketch: k * dim func() values, varying one coordinate at a time,
    give a cheap starting point for further optimization
    especially if func() is monotone, up or down, in each coordinate.
"""

from __future__ import division
import sys
import numpy as np
    # from https://github.com/SMTorg/smt  Surrogate Modeling Toolbox