# Questions tagged [constrained-optimization]

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### Compelling demonstrations/examples on ill conditioning of penalty methods

It's known that penalty methods in optimization suffer from ill conditioning. But is there simple yet compelling demonstrations/examples to teach this concept to convince and visualize for learners?
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### what is this general form of an optimization problem (Structural) representing?

I am currently reading this article by Sigmund. Sigmund, O., Maute, K. Topology optimization approaches. Struct Multidisc Optim 48, 1031–1055 (2013). https://doi.org/10.1007/s00158-013-0978-6 I ...
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### Minimum distance from point to surface

I’m looking for code that is well-suited to solving a fairly simple minimization problem: I have a reference point $\mathbf p$ in 3D space, and I want to minimize $\|\mathbf x - \mathbf p\|^2$ subject ...
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### Why slack variables for inequality constraints?

When solving constraint optimization problems with (primal dual) interior points methods, I often read (e.g. on slide 17) that one should not use the inequality constraints $g(x)\leq 0$ directly, but ...
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### Objective function for PDE-constrained boundary control problem in cylindrical coordinates

I'm interested in solving a boundary control problem for an axisymmetric diffusion problem where diffusive fluxes only appear radially. The corresponding problem for a uni-dimensional slab can be ...
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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 ...
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### 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 ...
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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 ...
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### 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 $Q$...
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### 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 ...
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### 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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### 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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### Expressing a Constraint in an optimization problem

If I have a vector of M "continuous" decision variables (say it is called x) , and if I want a constraint to express that only one of them is allowed to have a nonzero value (i.e. no more ...
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### Optimization problem

In the expression: $${\underset{\Omega}{\min}\left\|\beta A\Omega^{-1}B+C\right\|_{F}^{2}}\, ,$$ $$\text{subject to tr}(\Omega)=1, \Omega \ge 0\, ,$$ where ${\Omega}$ is nonnegative and symmetric ...
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### Efficient solver of a Integer programming

I am solving an Integer programming using MATLAB, yet the efficiency is low. Here is the problem: Suppose $v$ is a $N \times 1$ vector. For $v_i \in v$, $v_i \in \{0,1\}$. $D$ is a 0-1 matrix, which ...
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