Questions tagged [constrained-optimization]
The constrained-optimization tag has no usage guidance.
13
questions
2
votes
1
answer
68
views
Finding the minima of a multivariable function with constraints
I have a multivariable function (9 variables), and I want to find where the function records a minimum value. The function is as follows:
It also has a few constraints:
I tried a brute force ...
- 21
6
votes
3
answers
458
views
How do we formulate a problem where the decision variable has an index that is also a decision variable?
I want to maximize the sum of a nonlinear function $f(.)$ w.r.t. $x$ that is convex in $x$:
$$\max \sum_{i=1}^N f(x_i), $$where $x_i$ is a continuous variable and $0 \le x_i < 1$ for $i = 1, 2, \...
- 1,043
1
vote
1
answer
129
views
Formulating a continuous NLP problem with a class variable
In this minimization problem we have $N$ items, $j= 1, 2, \dots, N$ and a decision variable $x_j$ which are continuous values.
For every item, we have a nonlinear objective function $f$ in function of ...
- 1,043
5
votes
3
answers
2k
views
Genetic Algorithm
Is there any Python library as published on PyPi, with genetic algorithm (GA) or GA inspired solver that helps with constrained optimization?
I am aware of Matlab's GA solver and also aware that costs ...
- 3,310
4
votes
2
answers
466
views
Constrained optimization of a sum
I have to maximize the function $f= \sum_{i=1}^na_ix_i $ subject to the constraints $g = \sum_{i=1}^n x_i = 0 $, $-1\leq x_i \leq 1$ and $a_i>0$. Lagrange multiplier method doesn't work because $\...
- 143
2
votes
1
answer
211
views
Constrained Optimization Closed Form Solution Using KKT Gives Wrong Values
I have a (I guess) simple constrained optimization problem that I'm hoping to find a closed-form solution for using Lagrangian analysis and KKT conditions. I figured out the solution but there is one ...
- 245
2
votes
2
answers
98
views
Is there a name for this type of integer programming?
Let $x_i$ be a decision variable, and let $c_i$ be the coefficient for the decision variable $x_i$.
An integer programming problem is where the goal is to:
$\text{maximize} \quad \sum_i c_ix_i$
$\text{...
- 133
1
vote
0
answers
40
views
Is there a name for this type of integer programming? [duplicate]
Let $x_i$ be a decision variable, and let $c_i$ be the coefficient for the decision variable $x_i$.
An integer programming problem is where the goal is to:
$\text{maximize} \quad \sum_i c_ix_i$
$\text{...
- 133
3
votes
1
answer
166
views
Convex optimization with linear constraints. Can I solve it analytically?
I have a constrained convex optimization problem with linear equality and inequality constraints.
\begin{align}
\label{eq:costf}
\text{minimize}\ \
&f(x_1,\dots,x_m) = \sum_{i=1}^m \frac{1}{...
- 39
3
votes
2
answers
91
views
Augmented Lagrangian Function for Semidefinite Programming Problems
I am currently reading the paper "Alternating direction augmented Lagrangian methods for semidefinite programming" and was wondering about how one comes up with the Augmented Lagrangian ...
- 33
9
votes
2
answers
200
views
MINLP involving integrals, sparse matrices and CDF of random variables. Best environment?
INTRODUCTION
My research often involves solving MINLP problems with few constraints (usually two) and not many variables (say between one and three integer ones, and between one and five real-valued ...
- 191
5
votes
2
answers
192
views
Solve nonlinear programming problems practically
In an exam, I studied Theoretical approaches to converting constrained minimum problems into unconstrained minimum problems. Specifically:
KKT conditions
Projection Gradient Descent
Penalty and ...
Francesco Ladogana
24
votes
4
answers
11k
views
What are the advantages of commercial solvers like Gurobi or Xpress over open source solvers like COIN-OR or CVXPY?
I come from an ML background, and occasionally have to dive into the OR world. I am trying to figure out whether I need to purchase a commercial solver license for a certain problem set.
In the ML ...
- 2,089