# Questions tagged [optimization]

general questions about selecting a best element from some set of available alternatives.

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### Name of (and solution to) this generalization of linear assignment

I would like to know if the following problem is known and has any efficient solution. Given an $n\times n$ score matrix $S$. Find the best $a$ elements, in terms of their sum of scores, such that no ...
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### Would a machine learning algorithm benefit from an “optimization oracle”?

I'm trying to understand the behavior of machine learning algorithms where the loss function is non-convex and the problem of training the ML on a specific data set is computationally hard. Now let'...
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### Is it possible to approximate the solution of NP-Hard problems in polynomial time using linear programming? [closed]

Suppose we have a NP-Hard problem such as the k-col, which is meant to determine if a graph may be colored using at most ...
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### Are the intermediary sets in maximum cardinality search optimal in some way?

The maximum cardinality search (MCS) algorithm works as follows. Given a weighted graph $G = (V, E)$ where $w(u, v)$ denotes the weight of the edge $\{u, v\}$, we select a start node $a \in V$ and do ...
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### NP-Hard Knapsack Instances

Consider the classic Knapsack optimization problem (KP): Given $p_1, \dots, p_n, w_1, \dots, w_n, B\in\mathbb N$, compute a solution $I\subseteq \{1,\dots,n\}$, such that $\sum_{i\in I} w_i \leq B$ ...
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### Formalizing and optimizing constraints involving booleans, pairs of booleans, and integer sums

My scenario has various flavors of SAT, constrained quadratic pseudo-Boolean, and integer programming. My attempts to formalize and solve the problem with Z3's ...
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### Sum From A List Of Numbers (Algorithm) [closed]

I came upon a problem and have been trying to find a method more efficient then brute force, but I came up with nothing; and I am not even sure how to approach it... You have a list of numbers and a ...
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### Run Length eXtreme encoded length

In run length encoding (RLE) the code stream consists of pairs $(c_i,\ell_i)$, which is understood as writing the character $c_i$ repeatedly $\ell_i$ times. Consider the following "improvement" of ...
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### Minimum relevant variables in linear system - additive approximation

In the problem Minimum Relevant Variables in Linear System (Min-RVLS), the input is a linear system, e.g.: $$A x = b$$ and the goal is to find a solution $x$ with as few nonzero variables as ...
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### Pass ordering for greedy local search algorithms

Apologies in advance for the slightly general question - I'm really looking for pointers to research / good keywords to look for. I have a problem with the following setup: I have a (finite) totally ...
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### Back-propagation for computing derivative of certain line integral

Consider a function F (think of neural networks) with two sets of parameters: (1) model parameters $\mathbf{w}$, and (2) input data ${\bf x} \in {\mathbb R}^d$. Fix $i \in [d]$, consider the following ...
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### Best approach for allocation problem

I am a bit rusty on optimization algorithms and need an advice. This is my problem: I have n images (with width and ...
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### Problem property name where an optimal solution in a graph can be used as a solution in any subgraph

Suppose one is given a graph optimization problem where the optimal solution $S$ for the problem on graph $G$ can be used as a solution for any subgraph of $G$. In other words, given $S$ is an optimal ...
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### Shortest string in the intersection of regular languages

Inspired by https://codegolf.stackexchange.com/questions/53310/shortest-universal-maze-exit-string Each of the 138,172 valid mazes can be represented as a DFA with 9 states (including starting and ...
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### Linear optimization over intersection of totally unimodular matrices

I am currently dealing with a problem of the following form \begin{alignat}{2} &\underset{x, y \in \mathbb{R}^n}{{\text{min}}} && e^T x \nonumber\\ &\text{sub to} \hspace{0.05in}&&...
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### Optimal set union tree

Suppose we have a ground set of $n$ elements and $m$ sets are defined over them $S_i \subseteq [n]$. Think of the following procedure: At each step take two of the sets, take the union, and add the ...
Suppose a set function $f(S)$ is submodular and non-increasing, meaning that for any $S'\subset S$, $f(S') \geq f(S)$. The problem is to minimize $f(S)$ s.t. $|S| \leq k$. I am wondering if there are ...