# 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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### Methods for delaying the "break" in non-linear least squares optimisation when the step size gets too small?

I am using the Levenberg-Marquardt method for calibration purposes. Typically, the RMSE of my calibration looks like: I want to break the algorithm when the algorithm step-updates start to slow down, ...
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### references for optimization in the context of parameter identification with finite elements

i am performing parameter identification for a non-linear partial differential equation (elasticity) that I solve with finite elements. My optimization problem is a non-linear least squares data-...
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### Estimating/Tuning a Coefficient from a Quadratic Programming Objective Function so Optimal Solution Reflects Data

I am working on a problem that is a modified version of a two-knapsack knapsack problem. I am able to find the optimal choices by using Gurobi. However, I would like to estimate a coefficient that is ...
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### Optimization of the log-absolute: reformulating to DCP-compliant on Julia

I am trying to reformulate this optimization problem in order to get a DCP-complaint expression on Julia (I am using the ...
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### Faster convergence for minimizing least squares of forward modelling problems

This specific question was raised from optimizing parameters of column experiments in the hydrogeological context. I want to optimize a parameter of interest (in this case $D$), based on experimental ...
1 vote
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### Linear PDE solution with constraints

Consider the following linear PDE: $$\nabla_q V(q) - M_d(q)M^{-1}(q)\nabla_q V_d(q) = 0,$$ where $V(q)$ and $M(q)$ are known and $M_d(q)$ is a grey box function (e.x., $M_d(q)$ is fitted using a ...
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### What problems does softmax() solve and when should I think of using it - in simple terms

I just for the first time saw the function softmax() in this SO answer to How do I use a minimization function in scipy with constraints and was intrigued. Another way of weighting variables where ...
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### Optimizing multivariable without known function (only input & output), but it's a polynomial

I have multiple set of input (5 parameters) and output from an unknown function. But I know this is a polynomial function. What method can I use to optimize to find the polynomial variable that can ...
1 vote
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### Optimizing noisy but deterministic one-variable functions within an interval

I am looking for advice on what numerical methods to consider to solve optimization problems like the following, ideally with as few evaluations of the objective function as possible. I am looking to ...
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### Reuse linear mapping that provides the solution to least squares problem using LAPACK

LAPACK.gglse allows me to solve min x^T Q x s.t. A x = y (in my present use case, $Q$ is symmetric positive definite) without having to think about the numerical ...
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### Difference between minimizing a function by gradient descent and by norm minimization?

I have working on 2 ways of training a neural network. The first method uses gradient descent updates the model with Adam optimizer. the second method minimizes the norm of the gradient of the ...
1 vote
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I have a system $\vec{x}_{i + 1} = \vec{x}_i + W_i$ where $W = N(\vec{\mu}, \Sigma)$. For some matrix $H_i$, let $y_i = H_i$ and let $z_i = y_i + R$. Where $R$ is some random variable. We are given $... 2 votes 1 answer 92 views ### Min supporting line of a set of points I am following along Rourke's book and I am trying to do the excercies mentioned in this SO post: Min supporting line for a set of points Design an algorithm to find a line 𝐿 that: has all the ... 0 votes 2 answers 162 views ### Minimize ||AX - Y|| for a matrix A that lies in a special orthogonal group Let$X$and$Y$be two given$k\times n$real matrices. If$A$is a$k\times k$real matrix then$AX - Y$is a$k\times n$real matrix. Applying the Frobenius norm$\| AX - Y \|\$, we get a non-...
1 vote
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I am training a neural network with the multiobjective steepest gradient descent algorithm. The want to steer the direction of the gradient descent so that I land up at a point slightly above where I ...
1 vote