Questions tagged [constraints]

In mathematics, a constraint is a condition of an optimization problem that the solution must satisfy.

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Existence of global minimum $f(x,y,z) = x + y + z$ under the constraint $x^2+xy+2y^2-z=1$

The full exercise consists of (i) finding the minimum value of $f(x,y,z) = x + y + z$ under the constraint $g(x,y,z)=x^2+xy+2y^2-z=1$, and (ii) establishing whether the function has a maximum. I have ...
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Matching position and rotation of moving target.

So I'm trying to work out how to intercept a moving rotating target. The key is that that I must match both $x$, $y$ coordinates and the rotation of the target. I'm a little confused, as this must be ...
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Second-order cone constraints

If we have a system of constraints given by, $$Ax \preceq_K b$$ where $K$ is a second-order cone, would this simply be the same as requiring that: $$\|Ax\|_2 \leq b$$ where $\|\cdot\|_2$ is the $2$...
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How to convert a sum and product constraint into SMT-lib2

I'm wondering what the best way to convert a sum a le $$\sum_{v=exprLB}^{exprUB} 2 + exprContent(v) = 12.34$$ or similarly a product $$\prod_{v=exprLB}^{exprUB} exprContent(v) = 1234$$ into an SMT-...
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how to minimize constrained Frobenius norm equation

I’m trying to understand what is the exact process to minimize the following constrained Frobenius norm equation: $$||A-CW||_{F}^2$$ s.t. $$WW^T\ge D$$ I understand one possible way is to use the ...
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Optimization Software for mathematical models with (arg) min/max in constraints

With context of a college student timetable and course selection, I’m formulating a function that counts holes (the empty blocks of hour when there is no class) limited by the first course of the day ...
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What distributions can I simulate with this stochastic process?

For fun, I am trying to use a two-step stochastic process to simulate an existing distribution $\text{P}(x_i) = p_i > 0$ on some discrete set $x_1, ..., x_n$. The process is as follows. Pick an ...
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How do I formulate a sum constraint in quadratic programming?

I am attempting to solve a quadratic programming problem of the form: $$\mathrm{min} \ \frac{1}{2}\alpha^T G \alpha$$ $$\mathrm{s.t.} \ \sum_{i=1}^{n} \alpha_i y_i = 0$$ $$0 \leq \alpha_i \leq C$$ ...
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Spheres in higher dimensions …

Original Problem: For a given $y$ and $n$, I want to find all $x_i$'s that satisfy \begin{equation} \frac{x_1^2}{\sum_{i=1}^{n}{x_i^2}}=y \tag{1} \end{equation} while satisfying following ...
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Constrained optimization : Contour lines and Lagrange's multiplier

Basically the core of Lagrange's multiplier says that the solution to a constrained optimization occurs when the contour line of the function being maximized/minimized is tangential to the constraint ...
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Why not differentiate the Lagrangian w.r.t a lagrange multiplier?

I've heard from a reuptable source that it is problematic to differentiate the Lagrangian w.r.t the lagrange multiplier. I know that doing so is rather a waste of time since it just goves you back ...
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2 constraint optimization (Lagrange multipliers)

Determine the critical points of $x^3 + y^3 +z^3$, such that $x^2 + y^2 +z^2 = 1$ and $x + y+ z = 0$ by hand. Attempt at a solution: I seem to figure out $-1$ as the multiplier for $x+y+z=0$ but can'...
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Multivariable Calculus finding absolute extremas with constraints?

PART ONE: I know how to find extremas by just using the gradient of a function $\nabla f(x,y)=0$ But I have been given a function alongside a constraint equation. And I am immediately thinking to ...
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KKT conditions for L2 norm

I have the following minimization problem \begin{gather*} \text{minimize} \quad ||w|| \quad \quad w\in\mathbb{R}^2 \\ \text{subject to} \quad w_1+w_2+1\le0 \end{gather*} I would like to solve it ...
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Integer programming : how to express that one linear constraint implies another?

I have formulated a linearly-constrained integer optimization problem. For now, I have been solving it by using an exhaustive search approach over the integer variables. However, I would now like to ...