https://github.com/zang-langyan/mathematical-optimization
Mathematical Optimization Algorithms implemented in various languages (including Python, Julia, Matlab, R)
https://github.com/zang-langyan/mathematical-optimization
julia matlab optimization-algorithms python r
Last synced: 3 months ago
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Mathematical Optimization Algorithms implemented in various languages (including Python, Julia, Matlab, R)
- Host: GitHub
- URL: https://github.com/zang-langyan/mathematical-optimization
- Owner: zang-langyan
- License: bsd-3-clause
- Created: 2022-04-09T10:11:24.000Z (about 3 years ago)
- Default Branch: main
- Last Pushed: 2022-04-15T09:35:56.000Z (about 3 years ago)
- Last Synced: 2025-01-01T11:12:44.234Z (4 months ago)
- Topics: julia, matlab, optimization-algorithms, python, r
- Language: Python
- Homepage:
- Size: 25.4 KB
- Stars: 2
- Watchers: 2
- Forks: 1
- Open Issues: 0
-
Metadata Files:
- Readme: README.md
- License: LICENSE
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README
Mathematical Optimization
---
*Mathematical Optimization Algorithms implemented in various languages (including Python, Julia, Matlab, R)*
- [Mathematical Optimization](#mathematical-optimization)
- [Overview](#overview)
- [Examples](#examples)
- [Golden Section](#golden-section)
- [Python](#python)
- [Julia](#julia)
- [Matlab](#matlab)
- [R](#r)
- [Powell's Quadratic Interpolation](#powells-quadratic-interpolation)
- [Python](#python-1)
- [Julia](#julia-1)
- [Matlab](#matlab-1)
- [R](#r-1)
## Overview
- **Univariate Optimize**
- [Golden Section](#golden-section)
- [Powell's Quadratic Interpolation](#powells-quadratic-interpolation)
- **Multivariate Optimize**
- To be added
## Examples
### Golden Section
#### Python
```python
>>> import goldsec
>>> f = lambda x: x**2 + 4 * x - 4
>>> fConfig = goldsec.GoldSec(f, [-10,10], eps=1e-8)
>>> result = fConfig.GoldSection()
Optimization Results
-----------------------------------
-----------------------------------
Algorithm: Golden Section
Minimum point: -1.9999999770027157
Minimum: -8.0
Iterations: 45
>>> result
>>> result.argmin
-1.9999999770027157
>>> result.min
-8.0
>>> result.iter
45
```
#### Julia
```julia
julia> optfunc(x) = x^2 + 4 * x - 4;
julia> _GoldenSection_(optfunc, [-10,10], 1e-8)
Optimization Results
-----------------------------------
-----------------------------------
Algorithm: Golden Section
Minimum point: -1.9999999770027157
Minimum: -8.0
iterations: 45
Optim_res(-1.9999999770027157, -8.0, 45)
julia> _GoldenSection_(x -> 2x^2 + 3x + 1, [-10,10], 1e-8)
Optimization Results
-----------------------------------
-----------------------------------
Algorithm: Golden Section
Minimum point: -0.7499999977519514
Minimum: -0.12500000000000022
iterations: 45
Optim_res(-0.7499999977519514, -0.12500000000000022, 45)
```
#### Matlab
```matlab
>> [~] = goldsec(@(x) x^2 + 4*x - 4, [-10,10], 1e-4)
Optimization Results
-----------------------------------
-----------------------------------
Algorithm: Golden Section
Minimum point: -2.00
Minimum: -8.00
Iterations: 26
```
#### R
```r
> goldsec(function(x) x^2 + 4*x - 4, c(-10,10))
```
### Powell's Quadratic Interpolation
#### Python
```python
>>> from interpolation import *
>>> f = lambda x: x**2 + 100 * x - 4
>>> fConfig = Interpolation(f,lam0 = 0, h = 0.01, H = 2)
>>> result = fConfig.powells()
Optimization Results
-----------------------------------
-----------------------------------
Algorithm: Powell's Quadratic Interpolation
Minimum point: -49.999999999999915
Minimum: -2504.0000000000005
Iterations: 26
>>> result
>>> result.argmin
-49.999999999999915
>>> result.min
-2504.0000000000005
>>> result.iter
26
```
#### Julia
```julia
julia> optfunc(x) = x^2 + 100 * x - 4;
julia> _powells_(optfunc)
Optimization Results
-----------------------------------
-----------------------------------
Algorithm: Powell's Quadratic Interpolation
Minimum point: -49.999999999999915
Minimum: -2504.0000000000005
Iterations: 26
Optim_res(-49.999999999999915, -2504.0000000000005, 26)
julia> _powells_(x -> 2x^2 + 3x + 1)
Optimization Results
-----------------------------------
-----------------------------------
Algorithm: Powell's Quadratic Interpolation
Minimum point: -0.7499999999999996
Minimum: -0.125
Iterations: 2
Optim_res(-0.7499999999999996, -0.125, 2)
```
#### Matlab
```matlab
>> [argmin,minimum,iter] = interpolation(@(x) 3*x^2 + 150*x - 5, 0, 0.01, 1e-4, 2)
Optimization Results
-----------------------------------
-----------------------------------
Algorithm: Powell's Quadratic Interpolation
Minimum point: -25.00
Minimum: -1880.00
Iterations: 14
argmin =
-25.0000
minimum =
-1880
iter =
14
```
#### R
```r
> powells(function(x) x^2 + 4*x - 4)
```