# Questions tagged [optimization]

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

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### Iteratively minimizing the function

Consider the problem $$\min_{x\in X, y \in Y} f(x,y)$$ Can I solve the problem by iteratively solving the following two sub problems? x_{k+1} = \arg\...
58 views

### arithmetic formula simplication

Consider a function $f : \mathbb R^m \rightarrow \mathbb R^n$. Function $f$ can be written down as a simple arithmetic program. It uses addition, subtraction, multiplication and division - however, ...
551 views

### Is it possible to optimize the calculation of $ax+b$ once I know $a$ and $b$?

An "algorithm" for calculating $ax+b$ would take the steps Calculate $a$ times $x$ Calculate $b$ plus the result of previous line. But if the values of $a$ and $b$ are known, can we create a more ...
217 views

### Job scheduling: minimizing number of reads

Consider the following scheduling problem: input: set of computations $C = \{c_1, ..., c_n\}$ set of computing nodes $P = \{p_1, ..., p_n\}$ Dependency graph $D$ between jobs (DAG) $(c_i,c_j)$ ...
96 views

### Are there any approaches to the following scheduling problem?

Consider the following problem: we are given $K$ tasks $\langle n_1, n_2, ..., n_K \rangle$. Every task $n_i$ is qualified with two parameters: The time it takes to be completed ($t_i$) and, The ...
206 views

### Gilmore-Lawler bound for the QAP

I'm stuck with trying to implement the Gilmore-Lawler bound procedure for the quadratic assignment problem (QAP). That is, a bound one can use with a branch and bound algorithm to solve the QAP. I'm ...
2k views

### Existing benchmarks for scheduling problems?

Which benchmarks exist to evaluate the performance of algorithms for Job-Shop or Flow-shop scheduling problems?
257 views

### NP-hardness of a bilinear program?

Given $a_i, b_i, c_i, d_{ij}\in [0,1]$ for $i,j\in [n]$ and $i\neq j$ such that $\sum_{i\in [n]} a_i=1$ and $d_{ij}=d_{ji}$. I have the following bilinear program: max $\sum_{i=1}^n (x_i-a_i)y_i$ ...
214 views

### Is there a programming language where any arbitrary recursive function can be fused?

Compilers like GHC for Haskell use inlining as one of its most important optimising tools. Doing that is not possible for recursive functions, in general. A few techniques have been developed to amend ...
268 views

### Generating quadratic optimization problems amenable to quantum annealing

Some context: there is a current debate in adiabatic quantum computing over whether a particular machine, the D-Wave quantum annealer, can outperform a classical algorithm [*]. Earlier this year, a ...
440 views

### Optimization as LP on the convex hull of its solution space

I have heard claims that for a certain class of optimization problems, one can re-write the problem as a linear-programming problem on the convex hull of the solution space of the original problem (...
75 views

### Is it possible to formalize the notion of 'semi-greediness'?

It is commonly accepted that matroids provide an abstract setting for which greedy optimization works (although there are more general structures known as 'greedoids'). I was wondering whether there ...
631 views

### On the stopping criterion of coordinate descent method

I am trying to implement the coordinate descent method to solve the dual of linear SVM problem, but blocked at the stopping criterion. Consider the optimization problem \min f(\...
175 views

### Help with a special case for Hungarian algorithm

I am working on a problem and it appears to be a special case of Hungarian algorithm. In Hungarian algorithm for assignment problem, there are n people and n jobs. Each person can do any of n jobs ...
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### Quadratic Binary Optimization formulation of Steiner Tree problem

can someone point out to me a solution or give advice on how to formulate as efficiently as possible in terms of number of bits the minimum Steiner tree problem as a 0-1 quadratic optimization problem?...
119 views

### Looking for algorithm (or at least name) for this optimization problem

Suppose that we have $n \geq 2$ distinct triplets $t_0, t_1, ..., t_{n-1}$ of real numbers, $t_i = (x_i, l_i, r_i)$. Define $$\Delta(s) = \max_{i, j} \left[ s (x_j - x_i) + (r_j - l_i) \right]$$ The ...