# 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 59 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 538 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 258 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 226 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 45 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 374 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 86 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 56 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: $$\small\min_{A,B,C} \| Y_A - AX_A \|_F + \| Y_B - BX_B \|_F + \| Y_C - CX_C \|_F + \lambda_1 \|B - A^2\|_F + \lambda_2 \|C - A^4\|_F$$ ...