# Questions tagged [optimization]

Mathematical techniques for the selection of a best element (with respect to some criteria) from the set of available alternatives.

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### Optimal population allocation layout over the Earth

Does exist some model of optimal people occupancy over whole our planet? Something accounting for climate, resources (with and without existing settlements) availability, progress and grows ...
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### Stochastic Optimization

I am working on a Data Panel project that is about macro volatility, taking into consideration some quality indicators. According to my model, indicators definitely determine macro variables. Data are ...
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### Optimization with tax and deduction constraint

I want to find optimal demands for a utility function in the form: $$U_{1}(c_{1},c_{2})=c_{1}^{1-a}\cdot c_{2}^{a}$$ It is related to an altruistic behaviour, where $c_1$ is the consumption of the ...
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### Solving for parameter value

I have the following maximization function - $\max_{x \in (0,1)} (((p_1e_1x^2)^{r} + (p_2e_2(1-x)^2)^{r})/2)^{1/r}$ where, $p_1$ and $p_2$ are drawn from uniform distribution [0,1] and are considered ...
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### Algorithms/Models to solve minimal Matchings for consumer producer household pairs

I’m working on the following problem: Minimising the electricity price for household trading pairs. There’s producer and consumer households. Trades are just possible between producers and consumers. ...
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### Cost-optimal p2p-trade in a community of households

I’m trying to solve the following problem and I’ve been working on it for a long time already: I want to optimize electricity-costs in a smart grid. There’s producer and consumer households in the ...
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### Taking the partial derivative of the demand function

Define the demand function which maximizes x -> U(x) as: $\sum_{i=1}^n$$p_i$$\zeta_i$(p, I) = I According to my textbook if I differentiate this with respect to $p_j$ I will obtain, $\zeta_j$(p, ...
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### Is optimizing revenue and expense objectives simultaneously better than optimizing profit as composite objective?

In the profit maximization problem, I am curious if co-optimizing revenue and expense objectives simultaneously are better than optimizing profit (revenue - expense) as a single composite objective? I ...
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### Numerical Solution Using Excel about optimal consumption of households

I'm not sure how to solve this problem. I'm given the discount factor, interest rate, probability of high income shock, and various income shock sizes that I need to use to compute optimal consumption....
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### Finding the optimal consumption bundle given the strictly concave utility function $v(x,y) = U(x) +y$?

I am also finding it difficult to understand what are the fundamental differences between analysing optimal bundles between concave and convex functions ? Does it also happen that the optimal bundle ...