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Questions tagged [constrained-optimization]

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2 votes
1 answer
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Priority based demand fulfilment in Linear Constraint

Say I have 3 sources. D1, D2, D3. their capacity is 100, 200, 400. I want to create some constraints such that First D1 is depleted then D2 and then D3. But the catch is you cant use min or max ...
kunal chakraborty's user avatar
1 vote
2 answers
277 views

Efficient Algorithm for Scheduling 140 Predefined 1:1 Meetings with Variable Participant Constraints Over 7 Slots?

I’m tasked with organizing a large number (130) 1:1 meetings for 50 people across a limited number of time slots (7) during a conference. I am seeking advice on the best algorithmic approach to tackle ...
Toby's user avatar
  • 11
1 vote
0 answers
30 views

Optimal control problem with bounded control

Let's consider the following deterministic constrained optimisation problem, where $c(t)$ is the control, and $x(t)$ and $y(t)$ are the state variables: \begin{align} J(t) = \inf_{c(t)} \ &\int_0^\...
NC520's user avatar
  • 123
2 votes
1 answer
135 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 ...
KK29's user avatar
  • 21
6 votes
3 answers
473 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, \...
Steven01123581321's user avatar
1 vote
1 answer
133 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 ...
Steven01123581321's user avatar
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 ...
Sutanu Majumdar's user avatar
6 votes
4 answers
900 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 $\...
Deep's user avatar
  • 163
2 votes
1 answer
299 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 ...
Ibrahim Amer's user avatar
2 votes
2 answers
108 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{...
user avatar
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{...
user avatar
3 votes
1 answer
196 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}{...
newman_ash's user avatar
3 votes
2 answers
116 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 ...
benebrue's user avatar
9 votes
2 answers
210 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 ...
Vicent's user avatar
  • 191
5 votes
2 answers
228 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 ...
user avatar
29 votes
4 answers
15k 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 ...
Skander H.'s user avatar
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