# Questions tagged [constraints]

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### Differences in using Clausius-Duhem inequality vs Principle of Virtual Work/Power in derriving constitutive equations?

I am a novice getting my toes wet in continuum mechanics and nonlinear elasticity. I have seen papers that use both approaches in developing constitutive connections to compliment balance equations of ...
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### How to best code a problem with scipy, cvxpy or Convex.jl with given generated data

I have a curve fitting problem of the form: $$\textbf{y} = f(\textbf{x}, a,b,c,d) + \varepsilon$$ $$f(x, a,b,c,d) = \frac{b}{e^{x\cdot a}+c}+d$$ with the constraint \begin{aligned}...
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### Is there a way to bound the values of a variable when using scipy.integrate.solve_ivp in python?

I want to solve an IVP in python with two variables, x and u, but I need the values of u to be between 0 and 1. Right now it is giving me a solution with negative values for u. Here is the code I have....
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### Constraint programming problem with conditional constraints and some unknown indicator variables

I have an interesting little problem that I believe can be formulated in terms of optimization or constraint programming. I have a few dozen variables $a$, $b$, $c$ ... and a set of constraints that ...
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### Setting up optimization problem in GEKKO

I have the following dynamical system, $\frac{d \phi}{dt} = -M^TDM\phi \tag{1}\label{1}$ $\frac{d \hat\phi}{dt} = -M^T\tilde{D}M\hat \phi \tag{2} \label{2}$ $\eqref{1}$ represents the exact ...
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### How to get all intersections between two simple polygons in O(n+k)

Basically the formulation of the problem I'd like to solve is very simple. Given 2 simple polygons (without self-intersections) report all intersecting edge pairs in O(n+k) time, where n - is a total ...
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### Constraining the total volume in Finite Element Methods

I have a diffusion problem which can be broken down to be: $-\Delta u = f(u)$ on $\Omega ~/~ \Omega_{int}$ $u = 1$ on $\Omega_{int}$ Note that this is an internal Dirichlet constraint to the ...
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### Markov (Chain) image generators?

Markov Chains can be used to generate, or auto-complete, text. https://en.wikipedia.org/wiki/Markov_chain#Markov_text_generators Training text is read, and some information about the text is ...
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### sum of absolute difference constraint in optimization problem

I am writing a model for an optimization problem. I need to write the following constraint: $$\sum^{N - 1}_i \lvert (a_i - a_{i+1}) \rvert \leq 2\, .$$ How to write this constraint (or linearize)? ...
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### Semi-Definite relaxation of non-linear constraint?

I am implementing an optimization problem using semi-definite approach. One of my constraints is of following form $trace(A∗X)−(k∗trace(A∗X))+(k∗\sqrt {(trace(B∗X)} )==0$ where k is a constant, A ...
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### Nonlinear least squares with box constraints

What are recommended ways of doing nonlinear least squares, min $\sum err_i(p)^2$, with box constraints $lo_j <= p_j <= hi_j$ ? It seems to me (fools rush in) that one could make the box ...
335 views

### What is the mathematical and physical principle behind of RBE2 element？

I am writing a 3d linear finite element code to solve the standard linear elasticity equation on a tetrahedron mesh of a gearbox. Notice that, the two rectangular plates above the gearbox are fixed, ...
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### Convex Polygon Intersection

Determining the intersection of two convex polygons is one of the fundamental problems in computational geometry . I'm asking for an algorithm having: INPUT: Given two convex polygons P and Q in 2D (...
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### How does constraint resolution affect the stability/accuracy of numerical integration?

I understand some basic analysis techniques (local truncation error, global error, zero-stable, absolute stable, etc.) of numerical integration. But I find it hard to apply these techniques in ...
421 views

### Transform from constrained to unconstrained optimization

In a constrained optimization problem, I found in a paper a way to define new variables such that the constraints disappear. They only give the new variable definitions, and I would like to understand ...
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A consistency notion in constraint programming: Let $P = (X, D, C)$ be a CSP. Given a set of variables $Y \subseteq X$ with $|Y| = k -1$, a locally consistent instantiation $I$ on $Y$ is $k$-...