# Questions tagged [optimization]

This tag is intended for questions on methods for the (constrained or unconstrained) minimization or maximization of functions.

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### Difference between asymptotic and non-asymptotic convergence in optimization?

I am reading some optimization methods and I am facing some issues with two terms "asymptotic and non-asymptotic convergence". What is the difference between them?
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### Can constants and parameters in a Gekko model be simply Python variables?

I'm new to Gekko and I noticed that Gekko will still run even if I don't define fixed values in my model as Gekko constants and parameters. For example, this code still runs and gives an answer: ...
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### the convergence of the iterative algorithm has a major problem

In order to solve an optimization problem, I divided the main problem into two sub-problems. The two sub-problems require to be solved iteratively until the algorithm converges. I use the bi-section ...
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### Do we need smallest vectors to obtain the optimized solution in Gradient Descent?

I'm new to topics about optimization. I am currently reading about Steepest Descent Method in Gradient Descent optimization. I saw this equation where we need to find a new iterate with an initial ...
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### Formulating this optimization problem

Suppose I want to minimize below objective function $\sum | g(x_i) \cdot I_{g(x_i)<0} |^2$ i.e, the latter penalty terms like $|g(x_i)|^2$ are only computed when $g(x_i)<0$. $|g(x_i)|^2$ are ...
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### Optimizing a quadratic form integral over unit sphere

I have an optimization problem, which is to maximize the following integral over the unit sphere: $$\max_B \int d\Omega \mathbf{f}^{\dagger}(\theta,\phi) (B^{\dagger} + B) \mathbf{f}(\theta,\phi)$$ ...
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### Parameters estimation with fewer variables than parameters

I am trying to estimate parameters, 4 of them, by fitting a system of 3 ordinary differential equations. I am using a model published that was using 3 parameters and gave a good fit to the data, and I ...
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### Comparing minimas of two different functions

The goal is to find vectors $x_u$ and $y_i$, both of the same length $f=64$, and to do this the following loss function is minimized: $$\sum_{u, i} (1 + \alpha \cdot r_{ui})(p_{ui} - x_{u}^{T}y_i)^2$$ ...
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### Sample Average Approximation vs. Numerical Integration

In the sense of the calculation of the expected value of objective functions, we have two choices to evaluate the value; 1. Sample Average Approximation (SAA): $$\frac{1}{N}\sum_{i=1}^N f(x,\xi^i).$$...
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### Find coefficients in general second order differential equation

Suppose you have a system that can be described via the following equations of motion: $$\ddot{y}+\delta(t)\dot{y}+\alpha(t) y = \gamma\sin(\omega t)$$ The functions $\delta(t)$ and $\alpha(t)$ are ...
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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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### Binarization for optimization problems

I have a nonlinear mixed-integer optimization problem, and because of very high complexity when solving it using methods like Branch and Bound, I resorted to solve it using alternating method and ...
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### Adding a "cost term" to a linear regression, so solution values are minimized

I'm using Python's optimize.lsq_linear method to run a linear regression with the bounds set between 0% and 100% power usage. ...
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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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### How to generate neighbors for simulated annealing

I am learning about simulated annealing algorithm and want to create a general purpose one for optimizing continuous functions. The problem I have is how to generate the neighbor points as candidates. ...
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### Finding the extrema of a transition probability function for a quantum walker on a graph

The goal Implement some Python code to find the extrema points of a function that is strongly oscillating. The background Let $G$ be a connected graph with $n$ points with Laplacian matrix $L(G)$. We ...
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### Nonlinear root solving libraries which accept a Jacobian in band-storage

I'm in search for a library for solving large systems of non-linear equations, similar to MINPACK, but unlike MINPACK, can accept a Jacobian in band-storage. My Jacobian is sometimes not invertible, ...