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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4
votes
1answer
226 views

PuLP Transport Problem - How to add outcomes of decision variables together

I am working on a rail scheduling problem that moves product from a production plant to a storage facility to satisfy demand. I am new to PuLP so finding this difficult to understand why this isn't ...
4
votes
0answers
53 views

Identifying saddle point in constrained optimization

Suppose we are minimizing $f(x)$. The first order necessary condition of $x^*$ being local minmum is: $$\nabla f(x^*)= \mathbf{0}.$$ For sufficiency, we check if also $\nabla^2f(x^*) \succ 0$, i.e., ...
4
votes
2answers
284 views

What are the most useful evaluation metrics when comparing the performance of different model formulations

Suppose you are writing a paper about a certain new problem class. You have certain problem instances of different size (real-world as well as random) given. You developed different integer ...
5
votes
1answer
90 views

Local minimization of a function over a line

Let $f:\mathbb{R}^n \mapsto \mathbb{R}$ be a differentiable function. Suppose $x^*$ is a local minimizer of $f$ along every line that passes through $x^*$. This means that the function $$g(\alpha) = f(...
1
vote
0answers
85 views

How do I find the extreme rays and points for a stochastic programming problem

I have the following 2 stage Stochastic Programming program: \begin{align}\min_x& \quad x+\sum_{s=1}^{3}p_sQ_s(x)\\\text{s.t.}&\quad x\in\Bbb R\\&\quad Q_s(x)=\min\left[\begin{pmatrix}1&...
3
votes
1answer
94 views

Radial unboundedness vs convexity

We have a simple problem, namely minimizing: $$f(x) = x_1^2 + x_2^2 - x_1.$$ The gradient is $$\nabla f(x) = \begin{bmatrix} 2x_1 - 1 \\ 2x_2 \end{bmatrix},$$ hence the unique stationary point is: $...
1
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0answers
62 views

Combining Two Different Queues

I am trying to create an optimization model for a problem that involves two different types of queues. Given Poisson demand (for both), there is a queue with constant service time and another queue ...
5
votes
2answers
123 views

Minimizing $x_1/x_2$ over a simplex in the positive orthant

I need to solve the following problem \begin{align}\min&\quad x_1/x_2\\\text{s.t.}&\quad Ax \leq b\\&\quad x > 0\end{align} where $A$ is a positive matrix. The best thing I can think ...
8
votes
1answer
148 views

Heuristic Search Planning Tree Leading to Worse TSP Solutions than Naive Greedy

I'm doing a Traveling Salesman Problem (TSP) homework for a coursera optimization course. My first attempt was a regular naive greedy approach, from each point, moving to the closest node (that hadn't ...
8
votes
2answers
162 views

Modeling Linear Program to decide if an inequality is facet

Suppose you have a set of points $v_1,\ldots,v_n$, which are the vertices of the polytope $P=\operatorname{conv}\{v_1,\ldots,v_n\}$ and a linear inequality $a^\top v \leq b$. What would be a linear ...
4
votes
1answer
90 views

Analytically finding the maximizer of a trace optimization problem

$A \in \mathbb{R}^{m \times n}$ is an arbitrary data matrix. Moreover, $w \in \mathbb{R}^m$ is a data vector which is a probability vector, i.e., $w\succeq 0, \sum_{i=1}^m w_i = 1$. I have a ...
4
votes
1answer
87 views

How to convert non-normal probabilistic constraints to deterministic ones for mathematical modelling?

I am working on a chance-constrained optimisation model that takes into account uncertainty. I am aware of how to convert constraints that are of a probabilistic nature into the equivalent ...
3
votes
0answers
38 views

Best method to optimise the blending of different types of coal to ensure all quality parameters are met at the lowest possible price?

I am looking to optimise the blending of different types of coal for the coke making process of a steel plant. I want to take into account the statistical variation of each coal’s qualities, so for ...
4
votes
0answers
50 views

Confused in how to insert a slack variable in a constraint inequality

According to my understanding, we should put a slack variable to equate an inequality constraint by inserting the slack variable in the side that is less than the other side. For example, if we have $...
5
votes
1answer
123 views

Dual variables associated with same equation for different time instants

I have three equations that are essentially the same equation defined for three time instants. The equations are basically calculating the state of energy of an energy storage facility. \begin{align} ...
4
votes
0answers
50 views

Instructors optimized schedule task

I'm trying to solve one interesting math task. Let’s imagine we have a number of instructors with different timespans during the day in which they work or they are available. We need to display to ...
5
votes
1answer
87 views

How to linearize difference of absolutes?

How to linearize difference of absolutes? $$|a|\ge k|b|$$ where $a,b$ are variables and $k$ is a constant.
17
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3answers
371 views

Best ways to use machine learning / AI as an OR scientist

I have come across GUROBI's webinar "Mathematical optimization and machine learning". In essence, Mathematical Optimization (MO) and Machine Learning (ML) are different but complementary technologies....
2
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0answers
62 views

How to solve an LPP with summation

Up until this point I have only solved simple LPP problems with maybe 2 to 3 variables that looked like this, using pen and paper. I need to solve This Problem using Simplex, Dual Simplex, Big M and ...
6
votes
2answers
121 views

Is this another variant of Job Shop Scheduling Problem?

The problem is as follows: there are $n$ jobs $\mathcal{J}=\{J_1,\ldots, J_n\}$, each of which could be done. There are $k$ machines $M_1,\ldots,M_k$ that work in parallel, independently of each other,...
4
votes
1answer
367 views

How to read a solution file (.sol) in cplex python API?

I've been to trying to read a .sol file in cplex python API before solving the problem but couldn't find any command to do so. There are analogous commands for this ...
2
votes
0answers
63 views

Problem classification: optimal weights for Weighted Arithmetic Mean

I want to write an optimisation problem then solve it, to get optimised weights to compute a final score using a weighted arithmetic mean. The problem is as follows. I have an entity (an input vector ...
3
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1answer
113 views
5
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1answer
114 views

Which solver solves PSD constrained convex non-linear problem

I have a problem with a vector variable $w \in \mathbb{R}^n$ and a symmetric matrix variable $V \in \mathbb{R^{n \times n}}$. I am solving a problem which is roughly like: \begin{align} \begin{array}{...
6
votes
1answer
74 views

Maximum weight b-matching with global cardinality constraint

Suppose $A$ is an $n$-by-$n$ symmetric matrix whose entries are all nonnegative. $A_{ii} = 0$ for all $i$. We want to find an $n$-by-$n$ binary ($0/1$ valued) matrix $X$ that maximizes $$\sum_{ij} A_{...
4
votes
1answer
64 views

Optimize probability parameter in an optimal control problem

We have a game with infinite but countable rounds. We have one machine, that may either break down, or continue operating. For each round the machine operates, it gives cost $-1$ (so profit of $1$). ...
13
votes
3answers
211 views

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 ...
16
votes
7answers
2k views

Does there exist an aggregation of videos on optimization?

Is there a website or otherwise maintained list of talks regarding mathematical optimization? This would be a big help for the community it seems. I'm most interested in those relating to integer ...
4
votes
0answers
40 views

Help with constrained or regularized optimization problem involving variable matrices and powers of matrices (or perhaps matrix logarithms)

I am attempting to solve the following optimization problem: $$ \small\min_{A,B,C} \| Y_A - AX_A \|_F + \| Y_B - BX_B \|_F + \| Y_C - CX_C \|_F + \lambda_1 \|B - A^2\|_F + \lambda_2 \|C - A^4\|_F $$ ...
3
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0answers
60 views

Integer variable optimization - decreasing execution time

I have a variable declared as follows in AMPL: ...
8
votes
1answer
188 views

Can Gurobi or CPLEX handle nonlinearly constrained problems?

Though my title is quite general (please feel free to edit), indeed, I wonder if the following models can be solved in Gurobi or CPLEX. Model 2 is just an alternative one to Model 1. Although we ...
9
votes
1answer
279 views

Compute the distance from a point inside a convex set to the boundary of the set

Problem Let $\mathcal C = \{ X \in \mathbb{R}^n \mid g(X) \leq 0\}$ where $g$ is convex, and let $X_c \in \mathcal{C}$. Is there any algorithm to compute the distance from $X_c$ to the boundary of $\...
3
votes
2answers
114 views

Minimizing a variable over the intersection of simplex and linear constraints

I am solving: \begin{align} \begin{array}{rll} y^* = \min & y & \\ \mathrm{s.t.} & a_i^\top x \leq y, & i=1,\ldots,m \\ & x \succeq 0,\ \mathbf{1}^\top x = 1. & \end{array} \...
3
votes
1answer
100 views

Graphical illustration Excel

I have formulated a linear optimization model and solve it using the Excel Solver. How can I illustrate the slacks vs usage?
3
votes
1answer
249 views

Linear programming sensitivity analysis using Matlab

I have a linear program in the MPS file format listing all the rows, columns, right-hand sides, etc. I can read that in Matlab and solve it using linprog. However, it seems there is no easy way to do ...
8
votes
1answer
329 views

if-else condition for the objective variable using big M notation

Let $0\leq \beta\leq 1$ be an objective variable. The size of $\beta$ is $N\!\times\!N$. Now, how can I impose the following? if $\beta_{i,j}>0$ then $\beta_{j,i}=0$ Big M notation can be ...
3
votes
1answer
57 views

Iterative calculus with Excel - N° 2

In continuation with the previous post, I propose you another problem. I have this model: \begin{align}\min&\quad F\\\text{s.t.}&\quad F-(1150x_{B_{1}}+1000x_{B_{2}}+1350x_{B_{3}}-S_{1})=430\...
5
votes
1answer
405 views

How to run MOSEK solver in CVXOPT

I have written a small code to do a simple min variance optimisation using CVXOPT, you can see the whole code below By using solvers.qp(P, q, G, h, A, b) in CVXOPT ...
3
votes
1answer
239 views

Iterative calculus with Excel

I have this model: \begin{align}\max&\quad\small{(0.2(1.07)^{-1}+0.2(1.07)^{-2}+0.9(1.07)^{-3})x_A+0.4(1.07)^{-1}+0.5(1.07)^{-2}+0.3(1.07)^{-3})x_B}\\&\quad 0.2x_{A}+0.4x_{B}\geq300\,000 \\&...
2
votes
0answers
65 views

How to find minimum number of locomotives to cover maximum miles in a network?

I have a freight train dataset with details like locomotive type, substations it passes through, trip date, travel miles, etc. There are 5 locomotive types in the dataset, and each type has 20-30 ...
3
votes
2answers
223 views

Convexity of a function

I would like to show that this function $$2x^2 + 8y^2$$ is convex or concave by using the definition $$f(θx+(1−θ)y) \le θf(x)+(1−θ)f(y)$$ From my understanding, using the Hessian matrix, I believe ...
4
votes
3answers
166 views

Problem Clustering and Suggestions for Solving it (Job-Shop?)

I am trying to find the amount that an item may get produced. To produce this item I need casting-molds. A casting-mold can be used multiple times after it becomes available again. For the ...
4
votes
1answer
47 views

Access LpVariable as input to another Keras sequential network

I want to use LpVariable as an input argument to a sequential CNN network layer, which is in Keras. When I tried to call the function I got the error as follows: <...
10
votes
2answers
174 views

Use integer/quadratic programming to maximize consecutive zeros in a binary array

A binary array $t = [t_1, t_2, t_3, t_4, t_5]$ with each element a binary integer variable taking values 0 or 1. You can think this vector as slots with 1 representing the slot being taken and 0 ...
3
votes
0answers
46 views

Discrete optimization in transport economics

I was working on a problem in transport economics where the optimal number of trips in a given duration of time is to be found out. The profit is a function of the price vector $p$ and time cost $c$ ...
9
votes
1answer
112 views

Scheduling events in order to maximize preparation time

Problem statement I'm given a set of events $E$, and $\forall e \in E$ also: a set of plausible dates on which the event can happen $D_e$ importance (weight) $w_e$ ideal preparation time duration $...
6
votes
4answers
155 views

Sequential quadratic programming source

What are the good text books to learn SQP? Are there any online courses that you can suggest?
9
votes
1answer
177 views

How to classify and model this problem?

I was given the task to model the following problem and find a solution for it, but as I do not have any experience in this field, I already have trouble classifying it. There are a number of ...
11
votes
2answers
1k views

Linear programming: objective function with “buckets”

I had a linear programming problem with the following objective function $$f(x) = \sum_{j}x_jq_jp_j - \sum_{i}\left(\sum_{j}x_jq_jC_{ij} \right) c_i$$ Where $q, p, C, c$ are known. This problem was ...
6
votes
1answer
89 views

How to minimize a weighted sum of RMSE-like terms?

I am trying to solve the following problem: \begin{align} \min&\quad f(x) = \sum_{i=1}^{n}{a_ix_i} + \sum_{i=1}^{n}{b_i\sqrt{\sum_{j=1}^{m}{\left(y_{i,j}-x_i\right)^2}}}\\\text{s.t.}&\quad x_{...

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