# 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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### Armijo Line Search Parameters

I am trying to compare many unconstrained optimization algorithms like gradient method, Newton method with line search, Polak-Ribiere algorithm, Broyden-Fletcher-Goldfarb-Shanno algorithm, so on so ...
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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 ...
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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\... 0answers 87 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 ... 0answers 60 views ### 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);&... 0answers 546 views ### 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 ... 0answers 120 views ### 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 ... 0answers 52 views ### 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 ... 0answers 260 views ### 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 ... 0answers 55 views ### 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 ... 0answers 229 views ### 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 ... 0answers 46 views ### 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 ... 0answers 386 views ### 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 ... 0answers 124 views ### 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 ... 0answers 34 views ### 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. ... 0answers 193 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 ... 0answers 87 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}... 0answers 56 views ### Identifying saddle point in constrained optimization Suppose we are minimizingf(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., ... 0answers 59 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$...
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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 ...
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### 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: $$\small\min_{A,B,C} \| Y_A - AX_A \|_F + \| Y_B - BX_B \|_F + \| Y_C - CX_C \|_F + \lambda_1 \|B - A^2\|_F + \lambda_2 \|C - A^4\|_F$$ ...
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### Constraint equivalence in PuLP

I'm working on an optimization problem in PuLP and I have to enforce a daily minimum of shifts and a daily maximum of assigned shifts. I have the following constraints to ensure each day has a minimum ...
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### 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 ...
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### Integer variable optimization - decreasing execution time

I have a variable declared as follows in AMPL: ...
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### 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 $c$ ...
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### How can I do this in GAMS?

I am mimicking a GAMS model that was introduced in Soler et al. (2013)1 to compare my new model with its results. In a nutshell, assume we have a variable $t$ that is supposed to only take certain ...
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### How can I find the shortest path solution or even begin to finding the most optimal solution to a weld robot sequencing problem?

Not sure this belongs here, but I thought I'd ask: How should I come to an understanding of an optimal weld sequence for a weld robot that welds a physical item on a revolving carousel (the gray T ...
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### Building model takes so much time in Cplex

I am a beginner in CPLEX. I have a model with about 1 million constants and 800k rows and 1.6 million columns. I implemented in both GAMS and CPLEX (C# as the platform). The final solution for both is ...
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### Problem with Piecewise constraint in Gurobi

I am facing a problem in my model with piecewise constraints that is making my one of the decision variables equal to zero for every value. My objective function is: \begin{equation} \min \sum_{t=...
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### How to interpret this problem of multicriteria decision

I am trying to optimise a cost function that consists of three parameters (A,B,C) using weighted sum approach for the selection of optimal technique out of three techniques. Parameter A unit is in ...
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### Minimising average holding cost per unit time is equivalent to minimising average delay per customer in queue

This question was originally asked on Math Stack Exchange. It is probably better suited here. Introduction When one thinks about a queue, it is natural to want to find a policy that minimises the ...
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### Multiple Depot/Crew Office Bus Driver Scheduling Modelling

I'm working on Bus Driver Schedule with multiple add-on constraints that are complex and hence trying to figure out how this can be achieved. Reference of Bus Driver Scheduling using OR-Tools:- https:/...
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### How to use NEOS without using Pyomo

I am new to modelling language and specifically NEOS server. I aim to solve MINLP using Baron, through the NEOS server. So, far I have been able to write model file, data file and command file as ...
Suppose there are $x$ servers, and $y$ users. The $y$ users are to be assigned to the $x$ servers similar to classic scheduling problems. The cost of using servers is given by $c(|x|)$ which is an ...