# 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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### FEM : energy minimization VS PDE solving

Engineering FEM When I studied engineering, I learned the traditional approach for finite elements for elasticity. The point was to solve the PDE $-div(\sigma)=f$ as: Multiply your PDE with a test ...
78 views

### 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?
102 views

### 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 ...
113k views

### Is there a high quality nonlinear programming solver for Python?

I have several challenging non-convex global optimization problems to solve. Currently I use MATLAB's Optimization Toolbox (specifically, fmincon() with algorithm=<...
27 views

### 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: ...
24 views

### 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 ...
27 views

### 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 ...
83 views

### 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 ...
116 views

### R function or package for carrying out maximum likelihood techniques in random effect models

I am applying optim() function in R to obtain maximum likelihood estimates of the fixed effects and random effects in a model with bivariate random effects. The ...
102 views

### Optimizing a quadratic form integral over unit sphere

I have an optimization problem, which is to maximize the following integral over the unit sphere: $$\max_B \int d\Omega \mathbf{f}^{\dagger}(\theta,\phi) (B^{\dagger} + B) \mathbf{f}(\theta,\phi)$$ ...
58 views

### 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: $$\sum_{u, i} (1 + \alpha \cdot r_{ui})(p_{ui} - x_{u}^{T}y_i)^2$$ ...
25 views

### 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): $$\frac{1}{N}\sum_{i=1}^N f(x,\xi^i).$$...
38 views

### 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. ...
83 views

### 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 ...
60 views

### 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 ...
65 views

### 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 ...
8k views

### Why should non-convexity be a problem in optimization?

I was very surprised when I started to read something about non-convex optimization in general and I saw statements like this: Many practical problems of importance are non-convex, and most non-...
49 views