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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Solving large-scale stochastic mixed integer program

What are some methods or algorithms for solving a large-scale stochastic mixed-integer optimization problem that runs on an hourly dataset for a year? Do we employ some kind of decomposition? (the ...
S_Scouse's user avatar
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KKT conditions validation- one dual variable equating to two values

I have the following optimization problem: \begin{alignat}2\min &\quad A(t)\cdot x(t)-B(t)\cdot y(t)+C(t)\cdot z(t)-D(t)\cdot k(t)\\\text{s.t.}&\quad z(t)+z_1(t)-y(t)-y_1(t)+x(t) = k(t);&...
S_Scouse's user avatar
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7 votes
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176 views

Relationship between two minimization problems

Let $\mathbf{A}$ be a ${n\times J}$ matrix with $A_{ij}\geq0$ (and $A_{ij}>0$ for most $ij$, there cannot be any rows or columns that consist only of $0$s), $Q=\left\{\mathbf{q}\mid \mathbf{q}\in\...
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Having trouble with objective function in Python: "GurobiError: Variable not in model". What else could I try?

I am trying to figure out how I can write this objective function into python using Gurobi. I have to minimize the sum of the product of three dictionary's values. The reason I am confused is that ...
Jacob Myer's user avatar
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95 views

Calculating robustness of layout plans

We have tried to design a manufacturing cell which will produce specific families of products. We figure out three layout plans for implementation. For practical reasons, we need to calculate the ...
A.Omidi's user avatar
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6 votes
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Water quality component optimization

I have an optimization problem that I'm attempting to tackle. As you can see in the image below, there's a graph network through which water flows. I've drawn out the problem in the image to explain ...
Nisith Singh's user avatar
6 votes
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Semi-definite Programming, non standard notation

The usual way to define a semi-definite program (SDP), e.g., as given in Boyd and Vandenberghe's convex optimization book, is: $$ \begin{array}{cl} \min & c^\top x \\ \mathrm{s.t.} & 0 \succeq ...
independentvariable's user avatar
6 votes
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How to make constraints satisfy disciplined convex programming guidelines?

How do I turn my convex constraints (described below) into constraints that are DCP so that I can solve them in CVXPy? Is there some ``cheat sheet'' of standard tricks? I'm trying to implement the ...
Dupin's user avatar
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5 votes
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201 views

How to use interpolation for problem parameters in Pyomo

I'm working on my first Pyomo DAE project to teach myself how to use it for trajectory optimization. I have generated an atmosphere lookup table with density and speed of sound as a function of ...
machalot's user avatar
5 votes
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What kind of packing problem is this?

I have the following problem which seems related to the packing problem. I have a grid of same size rectangles and a polygon on which this grid of rectangles needs to be placed such that the number of ...
Av0's user avatar
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Why do we use the square root as a proportional measure?

I originally posted this on the Mathematics Stack Exchange site, but I think it fits more on the OR-site. I'm reading a paper where the goal is to determine the weights of a weighted arithmetic mean ...
Steven01123581321's user avatar
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Reference request — fishery yield optimization

I'm looking for references to do a review of research on managing fisheries in industry. I've seen adaptions of population growth models which include some harvesting constant or function and was ...
Ryan Howe's user avatar
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Substituting inequality by equality constraints

Let $\mathbf{A}=\left(a_{ij}\right)$ be a $n\times J$ matrix with $a_{ij}\geq 0$, $n>J$ and such that no row or column has all its entries equal to zero. Let also $\mathbf{k}=\left(k_j\right)$ be a ...
Patricio's user avatar
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What is the difference between root relaxation and LP relaxation

(I apologize. I saw this question but, I do not know these may be the same or not.) I am trying to solve a MIP problem and have an issue about that. The problem's LP relaxation has the objective ...
A.Omidi's user avatar
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A good memoryless elevator strategy?

Could you OR whizkids please help me out with this one: https://stackoverflow.com/questions/61854621/a-good-memoryless-elevator-strategy Surely somebody has solved this before. How do you classify ...
Henrik4's user avatar
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Best method to optimize the blending of different types of coal to ensure all quality parameters are met at the lowest possible price?

I am looking to optimize 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 ...
danielcharters's user avatar
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In a binary logistic regression context, how to introduce a constraint to model the dependency between consecutive samples

Imagine we are running a logistic regression to identify opportunities for car sale promotion, using previous promotion campaign's result. Each $y$ is the increase of car sale after the promotion. ...
eight3's user avatar
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Any recommendations for learning about polyhedra and integer programming?

My knowledge on convex polyhedra and systems of linear inequalities (facets, edges, Farkas Lemma, projections, duality, etc.) is very scattered, and I'l like to go through a book to solidify it. I'm ...
user56202's user avatar
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Analytical solution of constrained quadratic program

I'm trying to solve a "simple" (= small) optimization problem often, with only minor changes to the objective function. Therefore it's important to keep the "time per solve" as low ...
kchnkrml's user avatar
4 votes
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Expected Value of Piecewise Exponential Function

I have the following distribution. $$\operatorname{logpdf}(x) = -\sum_{i = 0}^n \max(v_i \cdot x + b_i, 0) -1/2 (x - \mu)^T M (x - \mu) + \text{const}$$ Where $M$ is symmetric positive definite, $x \...
JEK's user avatar
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Does knowing the "correct multipliers" for globally optimal first-order critical points help you algorithmically?

Consider the following nonlinear optimization problem: \begin{align*} &\min f(x) \\ \text{such that } &h_1(x) = 0, \\ &h_2(x) = 0, \\ & \vdots \\ & h_m(x) = 0, \end{align*} where $...
lubob73's user avatar
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Understanding Optimal Transport Problems

I am trying to better understand the origins of Optimal Transport Problems such as Monge's Problem. For instance, I came across the following references: https://www.math.ucdavis.edu/~qlxia/Research/...
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Weighted nuclear norm minimization

The problem. Let $X,A \in\mathbb{R}^{n\times m}$ and let $W\in\mathbb{R}^{nm\times nm}$ be a positive definite matrix. I want to know if there is a closed-form solution to this problem $$ \min_{X} \...
Apprentice's user avatar
4 votes
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242 views

Simplified risk game: writing a pratical Minimax objective for mixed integer programming

Problem To ensure fairness of the game, I am writing a bot that plays against itself. I have trouble rewriting a minimax objective to a practical maximization in mixed integer programming. The amount ...
Qurious Cube's user avatar
4 votes
0 answers
184 views

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}...
runr's user avatar
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Mixing time exponent above threshold temperature for Glauber dynamics or annealing

It is well-known that the Glauber dynamics will converge in polynomial time to the Gibbs distribution for, say, the Ising model on a d-regular graph at high enough temperatures $T>T_c$. There are ...
user134977's user avatar
4 votes
0 answers
87 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., ...
independentvariable's user avatar
4 votes
0 answers
305 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 $...
John adams's user avatar
4 votes
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55 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 ...
BigGinDaHouse's user avatar
4 votes
0 answers
65 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: $$ \small\min_{A,B,C} \| Y_A - AX_A \|_F + \| Y_B - BX_B \|_F + \| Y_C - CX_C \|_F + \lambda_1 \|B - A^2\|_F + \lambda_2 \|C - A^4\|_F $$ ...
ARandomName's user avatar
4 votes
0 answers
71 views

Continue on "Is there a known MILP to schedule routes after routes are made"

I have made some progress on my previous question (Is there a known MILP to schedule routes after routes are made). I have derived the sets of the problem, which are: 1) Itineraries of vehicle: $i \in ...
dimboukosis's user avatar
4 votes
0 answers
1k views

cvxpy: Code that works for default solver doesn't work for cp.GLPK_MI

The following code works: ...
Rohit Pandey's user avatar
4 votes
0 answers
241 views

How can I formulate this multi-objective optimization problem?

Now, for each system $X$ $(X=A,B,C,E)$, my objective is $$\max\min\frac{s_{x_u}}{d_{x_u}}$$ here, $x=a$ for system A, $x=b$ for system B and follows... and for the whole system, my objective is $$\max\...
KGM's user avatar
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4 votes
1 answer
126 views

How to find the vectors to be added as the columns in the master problem of Dantzig-Wolfe Decomposition?

I have a Dantzig-Wolfe decomposition question with the following questions \begin{align} &Maximize: 2x_1 +3x_2+4x_3+2x_4 \\ s.t. \quad & x_1 +x_2+2x_3+x_4 \le 15\\ & x_1 +x_2+2x_3+...
Romio Rodriguez's user avatar
3 votes
0 answers
43 views

Adding synchronisation constraint in Prize-collecting VRPTW

I am solving a Prize Collecting VRPTW. In my problem, each node represents a visit that needs to be made within a certain time window, and the "prize" for each node is the time spent at the ...
orman's user avatar
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3 votes
0 answers
71 views

constrained optimization with decreasing constraint thresholds -Literature tips

consider a constrained optimization problem (typically c=0), with f highly nonlinear: \begin{equation} \text{minimize}_x f(x) \\\\ s.t \ \ \ \ g(x) \leq c \end{equation} I experimented a bit and found ...
Lukas Schroth's user avatar
3 votes
0 answers
81 views

Looking for an efficient way to solve a fractional problem (affine function over euclidean norm )

While working on optimization issues I encountered the following problem: $$\left\{\begin{array}{ll} {\displaystyle \sup_{z\in\mathbb{R}^{m}}} &\frac{ \langle c,z \rangle + \rho}{ \left\|B z\...
Diego Fonseca's user avatar
3 votes
0 answers
72 views

Pygmo2: What is the point of evolving an archipelago in a loop if number of generations already set in algo

I want to solve a multi-objective problem with nsga2 or moead taking advantage of the parallelism available in pygmo library. I have seen a very nice example on github posted below. However I am not ...
Sophie's user avatar
  • 31
3 votes
0 answers
94 views

Projected Gradient Ascent for linear programming

I need to find a reasonable maximum for a linear programming problem, for which standard solvers for linear programming are just too slow. I was thinking of using projected gradient ascent, but do not ...
Carol Eisen's user avatar
3 votes
0 answers
123 views

Creating Disjunctions for MIP Model. Code taking too long to execute

I am currently following this guide in the hopes of building a linear programming model in python and solving using gurobi. https://towardsdatascience.com/schedule-optimisation-using-linear-...
SevenArmy's user avatar
3 votes
0 answers
137 views

Does Gurobipy exploits sparsity of the optimization problem?

What happens when a (sparse) csr matrix / array is submitted to Gurobi (via Cvxpy framework in python). Does it exploit the sparsity Information about the matrix or ...
pqrz's user avatar
  • 460
3 votes
0 answers
49 views

Control variables and cofounding effects in stochastic programming/,model predictive control/reinforcement learning

How can we be sure that confounding variables/control variables don’t pickup the effect our decisions w.r.t decision variables had on the actual control variable? Since the term control variable ...
stewardbranson's user avatar
3 votes
0 answers
169 views

Testing the pyomo optimization model

I have a resource scheduling optimization model in Pyomo with 3 constraints and an objective. The model runs well for the minimization and maximization objectives. ...
Waqas Swati's user avatar
3 votes
0 answers
196 views

What can traditional graph cut methods do well, that deep learning cannot?

I have been fascinated by the rise and fall of graph cut algorithms in recent years, which I described in this question: Was there something specific that caused graph cuts to lose popularity in the ...
Nike Dattani's user avatar
  • 1,278
3 votes
0 answers
131 views

When and where the cutting plane method should be applied?

As the cutting plan algorithm is a method to strengthen the feasible space of the linear programming, specifically in the MILP problems to invoke the integer solutions, it may be a problem-based ...
A.Omidi's user avatar
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3 votes
0 answers
108 views

Multiserver Queue Theory Optimization problem

I have a design optimization problem where I need to connect a customer with a server via call. The scenario is as follows: Customer-1 is connected with $N$ servers out of a total pool of $P$ servers....
hm980's user avatar
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3 votes
0 answers
123 views

Is my understanding of rolling horizon correct?

I would appreciate any feedback on my understanding of "rolling horizon in optimization". I'll try to point out, what is my understanding of it. First in simple words: You have an ...
Andre's user avatar
  • 303
3 votes
0 answers
77 views

Linear program with an additional second-degree utility term

I would like to solve a problem obtained from a LP by adding a second degree term to its utility. A simple example would be the following (with $c_i > 0$): $$ \min xy - c_1 z_1 - c_2 z_2 \\ \...
ubalage's user avatar
  • 31
3 votes
0 answers
51 views

Constructive proof for the Hyperplane Separating Theorem (HST)?

HST is usually proven through the existence of a unique minimum-norm vector in a nonempty closed convex set. I think this is an existential proof. However, to actually apply the result in a real world ...
High GPA's user avatar
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3 votes
0 answers
187 views

Good book to get familiar with the key concepts of Operations Research for a person which didn't enjoy a good math education in university?

I am currently reading research papers on optimization problems in logistics and struggle to understand the math notation. Any good beginner friendly books you would recommend? This is the paper I ...
Eddiee's user avatar
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