# Questions tagged [optimization]

For questions involving mathematical problems that aim to minimize or maximize some objective function, possibly subject to one or more constraints.

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### How to build a GAMS model in python

I looked at the GAMS python API but the documentation only describing already predefined models (run .gms with some tweaking options). My question is now: Can I somehow build a gams model from scratch ...
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### How to develop a vehicle routing optimization package? [closed]

I would like to know how vehicle routing software optimizes routes? In demos of this software, they provide the optimal (or a good) route in just a few seconds or minutes with several nodes (maybe 50 ...
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### Flexible Job Shop with Preemption

I'm trying to solve a flexible job shop problem variant that has precedence constraints on jobs along with a few other issues. We have a MIP formulation and also a simulated annealing algorithm to ...
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### Why can quadratic functions over polyhedrons be minimized exactly in finite time?

I have heard it said that QP problems $$\min f(x) = \frac 12 x^TAx + b^T x$$ $$x \in P$$ where $A$ is a symmetric matrix and $P$ is a polyhedron can all be solved exactly and in finite time (or it can ...
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### Pyomo + Ipopt. Speed Issue

I am using Pyomo + Ipopt as solver to solve a NLP problem. The problem is not extremely complex in terms of dimensionality and ...
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### Divisibility constraint in Integer programming

I have a simple question regarding the divisibility in integer programming suppose the objective function is $\text{max}\quad x_1 + x_2$ where the constraint is that the sum of $x_1$ and $x_2$ are ...
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### confusing results of two models with different complexity

i have two models that address the same problem. the first one is : the second one is: for different instances for the same size (n=30) i found the following results ( the first column on the left ...
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### Protein folding and protein design relation

I understand from this active COVID-19 question: Are there any COVID-19 (coronavirus) related optimization problems with input datasets that we can "crowd solve"? that the protein folding ...
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### Are there any real-world problems where quadratization helps to solve something that couldn't have been solved without quadratization?

The closest thing I know is the computer vision problem, in which an image is de-blurred and/or de-noised by quadratizing a quartic problem into a quadratic optimization problem (QUBO) and then the ...
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### How to determine the size of a model?

I want to know about the number of variables and constraints of this formulation (exp: $o(n)$ variables and constraints or $o(n^2)$ ....). Is the number of variables $\mathcal O(n^3)$ because we have ...
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I have a modified assignment problem for which I'm having difficulty formulating the constraints mathematically. I have a set of workers and a set of tasks which should be completed in the minimum ...
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### Which method to use to solve this multi-objective conflicting objectives

I have the following multiobjective problem. I need to minimize the user-perceived latency while doing so aggressively minimizing user-perceived latency generates large switching cost (Reconfiguration ...
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### Fast solvers for LASSO-type non-convex optimization problems

Given $y \in \mathbb{R}^{n \times 1}, X \in \mathbb{R}^{n \times p}$, $p > n$, assume a LASSO-type optimization problem in the form of  \hat\beta=\underset{\beta}{\operatorname{argmin}}\frac{1}{2}...
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### Optimizing MIP Parameters For Various Data Sets

I have a MIP that runs for several different data sets. For each data set the MIP runs multiple times, once for each time period in the data set, and each time period is independent. I've experimented ...
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### Recommended books/materials for practical applications of Operations Research in industry

I have a Masters' degree in Mathematics. I've very fair understanding of methods and techniques of Operations Research. I am looking for a good book/material where I can see a lot of examples on Math ...
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### how to apply Big M to model the logic constraint （if-then-else）

I was hoping to get some help in modelling the following logic as an MIP Constraint c_{m,l}^{RC} is binary decision variable. Simplify it：
### $\nabla_y\nabla_vf(x^*)\geq0$ for any concave $f$ if and only if $y=-v$
$f:\mathbb R^3\to\mathbb R$ is an arbitrary concave function. $H$ is a plane. $v$ is a given vector on $H$. $x^*=\max_{x\in H} f(x)$ Prove that $\nabla_y\nabla_vf(x^*)\geq 0$ if and only if $y=-v$. I ...