Questions tagged [constraints]

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

536 questions
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Concave/Convex Function rate of increase

I have the following constraints: $$\sum_{i=1}^2 p_i =2P$$ $$\sum_{i=1}^2 \gamma_i =2\Gamma$$ and the function $R$ which is strictly concave w.r.t. $p$ and strictly convex w.r.t. $\gamma$. How do I ...
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Minimize distance given other distance constraints

I want to minimize the Euclidean distance between a pair of points $\mathbf{P}_1, \mathbf{P}_2$ by finding a new point $\mathbf{P}_{2*}$, with the inequality constraints that for each $R_i$ of a set ...
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Given that $|3x|+|2y| \leq 1$ then the maximum value of $9x+4y$ is ?.

Suppose that $|3x|+|2y| \leq 1$ then the maximum value of $9x+4y$ is?. I thought of drawing the region satisfied the constraint given on the $xy$ plane. here is the region enclosed the lines - I ...
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If one is trying to maximize(or minimize) the Lagrangian $$\mathcal{L}(x,y,\lambda) = f(x,y) - \lambda \cdot g(x,y)$$ its fairly straightforward that this is achieved by solving: $$\nabla_{x,y,\... 1answer 76 views Maximize a table I am studying the max-sum algorithm to solve Distributed Constraint Optimization Problem. I have a very basic doubt about the maximization of a function w.r.t. a single variable. Consider the ... 1answer 116 views Log transformation in constrained optimization In constrained maximization, should I log-transform the constraint if the objective function is log-transformed?$$\max_{x, \ y} \,\, x^\alpha y^{1 - \alpha} \qquad \text{s.t.} \qquad p_x x + p_y y \ ...
Let $\mathcal{X} = \{x_1,\dots,x_N\}$ be a finite set in $\mathbb{R}^d$ and let $S$ and $D$ be two subsets of $\mathcal{X}\times \mathcal{X}$, with $S \cap D = \emptyset$. If $M$ is a positive ...