Questions tagged [constrained-optimization]
Questions about optimization problems subject to additional constraints.
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Estimating the rate of convergence of Projected Gradient Descent on constrained polynomial objectives
I am estimating the order of convergence of Projected Gradient Descent (GD) on quadratic polynomials with random coefficients independently drawn from Uniform(-1,1) and bounded by a unit hypercube. I'...
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Is the NLP formalism sub-optimal for real-world problems
My home-brew optimization studies have raised yet another fundamental question. The Nonlinear Programming formalism, "minimize f(x) subject to inequality and equality constraints, and x ...
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Iterative Solvers for Linear Least Squares with Integer Constraints
The classical linear least squares problem reads $\min_{x\in\mathbb{R}^n}\|Ax-b\|^2_2$ and its solutions satisfy the normal equations $A^{\top}Ax = A^{\top}b$. A standard approach to solve the latter ...
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BFGS Constrained Optimization Failure Due to Precision Loss
I am trying to optimize the following objective function according to some constraints. However, the optimization fails at the first iteration with the message that the desired error was not ...
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How conservation of momentum is ensured in (Projected) Gauss-Seidel constrain solver
I'm developing molecular dynamics where my time-step is limited by stiffness of the bonds. I trying to get inspiration from game-engines, where they solve similar problem (hard bond constrains). These ...
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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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Constraints involving max in ILP
Consider $n$ apps and $m$ transactions. $x_{ij}$ is a binary variable, it takes 0 or 1. $x_{ij}$ takes 1 if $i$th app is used for $j$th transaction, else 0.
min $\sum_{i=1}^{n}\sum_{j=1}^{m} x_{ij}$
...
- 111
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The nitty-gritty details of augmented Lagrangian methods
I am trying to implement (constrained) minimization of a certain function with the augmented Lagrangian method. Where can I find a reference that discusses in detail the good practices for the various ...
- 11.8k
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Name this optimum-within-convex-hull algorithm: State is a convex combination of hull vertices; Nonnegativity ensured by reparameterization
I'm looking for the "official" name(s) for a procedure for optimizing a convex loss function over a convex subset. This seems to be a default/naïve algorithm that folks come up with before ...
- 153
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Find a minium value of a function with discrete parameters, but some combinations are invalid
I'm not a mathematician, so sorry if I miss some obvious stuff. I'm trying to develop a bot for StarCraft 2, in particular the army control for it. For every army of the enemy, I want to find the ...
- 111
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Beyond the LP relaxation of binary least squares
I have a binary quadratic program with a convex objective function, of the form,
\begin{align}
\text{minimize}\;\;& x^tAx+b^tx\\
\text{subject to}\;\;& x_i\in\{0,1\}
\end{align}
where $A$ is ...
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Implementation of the roller constraint
What could be the best way to implement the roller constraint in finite element code, i.e. constraint of the type
$$\mathbf{u} \cdot \mathbf{n} = 0$$
I plan to enforce it in the weak sense by ...
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