Questions tagged [nonlinear-programming]
Questions about the theory and numerical algorithms for optimizing (minimizing or maximizing) nonlinear functions, possibly subject to equality and/or inequality constraints.
146 questions
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References on equality-constrained matrix-free inexact SQP
I want to implement an equality-constrained SQP method for a fairly large and sparse problem. As such I need to use iterative solvers where my matrix-vector products are matrix-free. Also I compute my ...
- 3,021
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Fitting a spherical surface given points with known distances from the (unknown) surface
There are numerous techniques to fit a sphere (with unknown centre and radius) through points in $R^3$, such that the fitted sphere passes through the points as closely as possible (in the least-...
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optimizing piecewise linear objective functions (perhaps non convex) with equality constraints
When I do my project, I need to optimize piecewise linear objective functions (perhaps non convex) with equality constraints.
The piecewise linear objective function may be not convex like this in the ...
- 11
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min(f(x)) is convex or concave based on type of f(x)
i have f(x) that is concave function. My question is g=min(f(x)) is concave or convex? And max(g) is concave or convex? there is a theorem for this?
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How to show that the solution of the following quadratic programming is non-negative
I have the following quadratic problem:
$max$ $a^Tx+0.5x^TAx$
$s.t: 1^Tx=1$
in which $a=[a_1, a_2,...,a_n]$ is a non-negative vector, and $1^T=[1,1, ..., 1]$. The hessian matrix $A$ has the ...
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Python code of explicit method of a nonlinear a BVP
I am trying to have a Python code for the following nonlinear BVP:
$$\frac{\partial N}{\partial t}=\frac{\partial^2 N}{\partial x^2}+N(1-N)-\sigma N$$ $$N(0,x)=\sin(2\pi x)$$
$$N(t,0)=0 \hspace{3mm}N(...
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Can we get the exact solution of large-scale quadratic programming problems (quadratic objective, linear inequality constraints) using KKT condition?
Crossposted at MathOverflow
Consider a quadratic programming problem with the following format:
$$
\text{min} Q(x) = c^Tx+\frac{1}{2}x^TDx \\
$$
$$
\text{s.t.} Ax\leq b, \\
x\geq 0
$$
where $D$ is a $...
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A question related with $p$-Laplacian and conjugate gradient method
I have the following energy functional of $p$-Laplacian equation:
$$
E(u) = \frac{1}{p} \int_{\Omega} |\nabla u|^p dx
$$
for $2.8 \leq p \leq 5$.
My goal is to minimize the energy functional by using ...
- 143
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Automatic differentiation necessary for large optimal control problems?
I am investigating ways to solve an optimal control problem in an embedded way, preferably in Java. The system is modeled with triple integrator dynamics $u=\dddot{x}$ and solved with multiple ...
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RobOptim for real-time computation
Do you think that the RobOptim optimization library (which I read about in C++ library for nonlinear constrained minimization) could be used for real-time optimization for the velocity control of a ...
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Solving the non-linear Hamiltonian using Scipy's root finding method
I am a complete novice to computational physics and am finding difficulty in implementing a code to iteratively solve for a $2\times2$ nonlinear Hamiltonian using Scipy's root solver. I can't seem to ...
2
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1
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202
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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 \\
...
- 121
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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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How to implement large rotations in total lagrangian formulation (nonlinear FEM)?
I have developed an Octave script to solve the nonlinear Euler-Bernoulli beam equations with linearized von Karman-strains, i.e. higher-order terms are dropped. The simulation results agree with ...
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Fitting data with a Voigt function
I have some data, (xrd data), that I would like peak fit with a pseudo-Voigt function, a combination of a Gaussian and a Lorentzian function. These are the functions
$G(x) = I \exp\left( -\frac{4\ln(2)...
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