# Tagged Questions

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### Smallest value taken by a quadratic polynomial in two variables.

Let $p$ be a degree $2$ polynomial with integer coefficients, say $$p(x,y) = Ax^2 + By^2 + Cxy + Dx + Ey + F.$$ I would like to find an algorithm which solves the following: Problem 1: Given ...
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### k- maximally link disjoint paths and equations

This problem is NP-complete and also discussed to some extent in Graph problems which are NP-Complete on directed graphs but polynomial on undirected graphs from the level of my reading from various ...
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### Alternative to Hungarian Algorithm to determine minimum cost?

Is there a graphic calculator (CAS technology) method to solve minimum cost problems/allocations that are normally completed with the Hungarian Algorithm... Hungarian Algorithm is time consuming, ...
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### How to load warehouse pallets efficiently?

Assume that we would wan't to develop a warehouse management system, which picks up plastick boxes and stacks them on a pallet. A pallet has a maximum of 5 vertical box stacks and the maximum height ...
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### How can I find the point (X, Y, Z) which minimizes this quantity?

I have a number of equally powerful light sources $L_i, 1 \le i \le N$ at points within a cube $(x_i, y_i, z_i), -1 \le x_i, y_i, z_i \le 1$. The intensity of each light falls off with distance ...
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### Largest Equilateral Triangle in a Polygon

Is there an algorithm to determine the largest equilateral triangle in a convex polygon?
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### How to efficiently compute the pareto front in a >2 dimensional multi-objective case?

I'm currently working on an optimization problem with 4 different objective functions and need an algorithm to compute the pareto frontier from several "solutions" to that problem. I already found ...
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### Global optimization

Assume that I want to find the global minimum of a non-linear, non-convex, multidimensional function subject to several restrictions. Could you recommend me any deterministic strategy which can ...
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### How to determine if a convex polytope is contained in a union of convex polytopes?

Given that we are in a Euclidean space of dimension d, that we have a bounded convex H-defined polytope P, and N possibly unbounded convex H-defined polytopes, I am looking for an "efficient" ...
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### Connected graph where edge costs depend on a parameter $t$. Find the $t^*$ which gives the minimum cost minimum spanning tree.

The set-up: Let $G=(\,V,\,E\,)$ be a connected graph. Associated with every edge $e\in E$ is a cost/weight function $f_e(t) = a_e t^2 + b_e t + c_e$, where $a_e>0$. For a fixed $t$ we can define ...
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### How to recognize if an algorithm working on ordinal data will also work if the ordering is reversed?

Inspired by a comment on this question. Assume that I have an algorithm which uses ordinally scaled data. The algorithm in the original question was the solution of the Secretary Problem. It uses ...
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### Is there a name for this optimization algorithm?

I'm a software developer trying to design an optimization algorithm and I'm wondering if what I'm trying to do resembles any of these. There's a daunting number and rather than read each one, perhaps ...