# Questions tagged [constrained-optimization]

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### Efficiently solving SDP relaxation of an integer quadratic program

I have an integer quadratic program of the form, \begin{align} \underset{x}{\max}&\;\;\|Ax-b\|_2^2\\ \text{subject to}&\;\;x\in{\bf Z}\geq0 \end{align} I'm currently using the (admittedly ...
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### optimization problem with L2-norm constraint

I am currently trying to solve a regression problem, which leads me to an optimization problem. Say that we have measured data ($\hat{S}(\omega)\in \mathbb{C}^{N\times N}$), and each entry of this ...
43 views

### The condtion for Augmented Langrangian Multiplier

I am currently learning the usage of Augmented Lagrangian Multiplier to achieve my equality constraint. I have learnt from the https://en.wikipedia.org/wiki/Augmented_Lagrangian_method that I have two ...
70 views

I'm learning about ADMM by reading Boyd's paper Distributed Optimization and Statistical Learning via the Alternating Direction Method of Multipliers. The paper says that ADMM is an improvement over ...
56 views

### Linearize problem with absolute value

Is there any method to linearize the following optimization problem? \begin{align} min_{x,y} &~~ c~[x; y] \\ st &~~ \sum x\leq \alpha_1 \\ &~~ \sum |y|\leq \alpha_2 \\ &~~ \sum y= 0 \\ ...
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### Why is a elementwise max not DCP?

I am trying to formulate a convex optimization problem using CVXPY. Everything works, except a constraint that does not seem to follow DCP rules. Let $D \in \Bbb R^n$ be a decision variable and let $Q$...
56 views

### Cyipopt fails to converge for NLP problem which fmincon() can solve

I'm currently trying to implement a python script for solving a constrained nonlinear optimization problem with ~800 variables and 2 constraints, one linear and one nonlinear. There already exists a ...
187 views

### Python solvers for MINLP in Pyomo in Google Colab

I am looking for a MINLP solver that works with Pyomo models which can be used in the Google Colab environment. I have already found MindtPy but it doesn't work in google colab.
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### Sufficient condition for real roots of a polynomial of order $n>5$ with arbitrary real coefficients

I ask for help in solving the problem. I am developing an optimization program that selects the coefficients of a polynomial of order $n> 5$ so that all its zeros are just real numbers. And I ...
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1 vote
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### How to constrain the every optimized vector component to be nonnegative?

I am building a gradient descent model based on portfolio optimization. Currently, I have finished the model and am able to run it smoothly without any problem. However, there's one issue that I ...
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### Model and solve nutrition optimization problem: how to?

How to solve/assess the following problem? Given: $N$ ingredients like apples, bread etc. Mass of an ingredient $j$ is in this simplified model a sum of macro nutrients carbohydrates, proteins and ...
134 views

### Parametric nonlinear programming

I believe, I have a parametric nonlinear optimization problem. The non-convex constraints depend on some parameters, and I seek a solution that satisfies these constraints for all parameters in a ...
• 21
1 vote
228 views

### How to best code a problem with scipy, cvxpy or Convex.jl with given generated data

I have a curve fitting problem of the form: $$\textbf{y} = f(\textbf{x}, a,b,c,d) + \varepsilon$$ $$f(x, a,b,c,d) = \frac{b}{e^{x\cdot a}+c}+d$$ with the constraint \begin{aligned}...
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1 vote
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### How applying the gradient descent method for solving a least square problem can remove the blur from an image?

I got an assignment where it asked to implement (in MATLAB) the gradient descent algorithm in order to resolve an ill posed least square problem: $$\min_u \Vert Gu - f \Vert$$ where $u$ is the ...
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### How to determine guitar tones played as early as possible?

I want to detect chords on a guitar as early as possible, but my approach with a sliding window and a filter bank seems to introduce too much lag. Would required observation time decrease by using a ...
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### Good languages/packages for interior point optimization with non-linear constraints?

I'm currently using Python's scipy.optimize package to perform parameter estimation for a system of 10 ODEs. I have some observed data, and I'm trying to find the set of parameters which makes the ODE ...
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### How can I deal with optimization problems that have a sum of functions of Z as a constraint when Z is the quantity to be minimized?

I have a problem where I have to minimize a certain quantity $Z$ subject to the following constraints:- $w_1 + w_2 + w_3 = 1$ $\frac{f_1(w_1*Z) + f_2(w_2 * Z) + f_3(w_3 * Z)}{Z} >= k$ where $k$ ...
• 101
1 vote
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### Bipartite Euclidean Matching simple to implement approximate algorithm

I am looking for a simple to implement algorithm for the bipartite euclidean matching problem (or an implementation of any practical algorithm). I am aware of Agarwal's paper, but I would like to ...
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### Implementation method selection for sparse constrained linear least squares or quadratic programming

I need to slove one optimization problem of quadratic programming. The number of optimization variables is about 16,000. The constraints include equality constraints and inequality constraints. I have ...
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1 vote
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### Constraint programming problem with conditional constraints and some unknown indicator variables

I have an interesting little problem that I believe can be formulated in terms of optimization or constraint programming. I have a few dozen variables $a$, $b$, $c$ ... and a set of constraints that ...
1 vote
155 views

### Why is quadratic penalty method used for equaltiy-constrained optimization?

When one equality-constrained optimization is formulated, the method of Lagrange multiplier will be the choice for me. In Chapter 17 from the book Numerical Optimization, quadratic penalty method can ...
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### Can this simple quadratic optimization problem be turned into a simple eigenvalue problem?

I'm interested in a type of problem on this form $$\min_{x} x^{T}Ax+x^{T}b \quad \text{s.t} \quad x^{T}x=1$$ where $A$ is positive definite. As you can see, if it weren't for the $x^{T}b$ term in the ...
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### Balanced constraint

In several optimization problems, we found what we called the balanced constraint(c^T • x = z ) For exp: C^T • 1 = 0 (C is a binary Matrix) Can I have an intuitive explanation about the concept and ...
1 vote
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### How to speed up the Mixed-Integer Quadratic Program process?

Currently, I am solving a problem in the format: M is an integer as well. The problem that troubles me is that X is a vector in {0,1} with a size of 7000. I use the solver in https://github.com/...
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1 vote
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### What is the generalization of the resource allocation problem I'm dealing with here?

I'm dealing with a problem as follows: I have a finite set of money 𝑚 to spend over 𝑟 different raffles, and I need to spend approximately to my budget, with the goal of maximizing my probability ...
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