# Questions tagged [optimization]

This tag is intended for questions on methods for the (constrained or unconstrained) minimization or maximization of functions.

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### Difference between Dishonest Newton method and Very Dishonest Newton method

What is the difference between the Dishonest Newton method and the Very Dishonest Newton method? Is there a difference or do they mean the same thing? I have tried searching for this on the internet ...
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### How to solve the inverse problem of least-squares?

Focusing on following least squares problem: $$\min\limits_{V} \lVert Z - WV \rVert _{_F}^2$$ $$Z∈{R}^{m\times n},\quad W∈{R}^{m\times k},\quad V∈{R}^{k\times n},\quad k\lt m\lt n$$ This problem ...
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Problem description Given data at many time instance $t$, $$\min _{\alpha, \Lambda, \beta} \lVert y(t) - \alpha e^{\Lambda t} \beta \rVert_F$$ with $$\lVert \alpha \rVert_2^F = 1$$ where $y(t) \... 0answers 44 views ### Space covering optimization I have the following problem: In the space$E=\{1, 2, \dots, N_x\} \times \{1, 2, \dots, N_y\}$, I want to define$N_R$rectangles$R_k=\{x_k^0, \dots, x_k^1\}\times\{y_k^0, \dots, y_k^1\}$which ... 1answer 106 views ### Some proof that linear translations and rotations of a bound-constrained function are equivalent For example, I have a function to optimize: $$f_1(x,y) = x^2+y^2, \quad x_{lb}\le x\le x_{ub},\quad y_{lb}\le y\le y_{ub}$$ Then I apply rotation by$\theta$plus translation by$x_0$and$y_0$: $$f_2(... 1answer 104 views ### ill-conditioning I am struggling with the following exercise from the book of Nocedal, Numerical optimization, chapter 2, exercise 2.12: Suppose that a function f of two variables is poorly scaled at the solution ... 2answers 167 views ### How do I check if a loss function can achieve its minimum? For example, the convex function f(t)=e^{-t} doesn't achieve its minimum 0 on the real line. In a linear regression with p predictors X, the loss function f(\beta)=||Y-X\beta||^2 achieves its ... 1answer 131 views ### Can I convert CUDA core to CPU core and use it as cpu core while running any program? I was using Metatrader5 and have designed a strategy for trading using MQL5 programming language. While I was running a Strategy Optimization process, I saw the it will need 10,00= iterations or ... 1answer 47 views ### Conflicting definition of limit point This question was raised at a different place without sufficient answers. Definition 1: We say that a vector x \in R^n is a limit point of a sequence \{x_k\} in R^n if there exists a ... 1answer 257 views ### What is required of the objective function in order to use Gauss Newton method? From what I understand, the Gauss-Newton method is used to find a search direction, then the step size, etc., can be determined by some other method. In addition to that, are the following ... 1answer 41 views ### How to decide on what techniques to adopt in Genetic Algorithm optimization Does it really matter which techniques we use in the process of GA optimization? For instance, if I use the Roulette Wheel Technique instead of Tournament Method for selection, two-point crossover ... 1answer 345 views ### I've developed a derivative-free optimization method, looking for comments Here is the URL: https://github.com/avaneev/biteopt I've tested it on numerous global optimization benchmarking functions (included), and on real-world hyperparameter optimization problems I have. ... 1answer 187 views ### How to numerically minimize a functional? How to numerically minimize a functional, for example,$$J[y]=\int_{x_1}^{x_2}L(x,y(x),y'(x))dx$$An equivalent problem is to solve the Euler equation for this functional as a differential equation. ... 1answer 42 views ### Distribute sources among destinations There are n sources with the following positive volumes: p_1, ..., p_n and there are m destinations with the following positive volumes: q_1, ..., q_m. It is known that p_1+ ...+ p_n=q_1+ ...+... 3answers 775 views ### Finding the first N roots of transcendental equation I need to find the first n roots of the transcendental equation \begin{equation} F(k) = J_m'(kr)Y_m'(k)-J'_m(k)Y'_m(kr) \end{equation} for integer values of m and any r \in [0,1) where J' ... 1answer 546 views ### Defining a soft constraint in cvxpy I am using cvxpy to do a simple portfolio optimization. I implemented the following dummy code ... 1answer 116 views ### Nonlinear least-squares solvers vs. generic minimization A nonlinear least-squares problem with F:\mathbb{R}^m\to\mathbb{R}^n,$$ F(x) \to \min_x \quad (\text{in the least-squares sense}) $$really means minimizing$$ \frac{1}{2} \|F(x)\|^2 \to \min_x. $$... 1answer 107 views ### What is the fastest way to solve Ax=b (subject to constraints and an absolute term) I am trying to solve/optimize Ax=b in the least squares sense subject to box constraints; a few (less than 5) equality/inequality constraints; and an absolute function penalty (or some other ... 0answers 19 views ### How does the MADS algorithm work in practice Mesh Adaptive Direct Search (MASH) is an algorithm for black box optimization I want to understand an implement this method to solve some 2D multivariate blackbox function f(x,y), but am having ... 2answers 948 views ### What is the most appropriate derivative free optimization algorithm We can use random optimization/ derivative free/ direct search to find the minimum of some black box function f. If I have some 2D black box function, f(x,y) - which I know to be convex - what ... 1answer 319 views ### Linear constraints for L-BFGS-B I know L-BFGS-B only supports simple box constrains of the form: l_i \leq x_i \leq u_i, where l_i and u_i are constants. For my specific optimization problem, I need to specify some simple ... 1answer 805 views ### How to define the derivative for Scipy.Optimize.Minimize I am trying to use scipy.optimize.minimize to minimise a quadratic objective function: f(x) =x^\top Q x. As a start, I have successfully implemented this using the built-in Nelder-Mead Simplex ... 1answer 181 views ### CPU and GPU influence on task parallel execution performance This question is mainly about hardware, but also about software. In my current work I have approximately 68 millions of combinations that I am iterating through, in parallel. For each of those ... 0answers 42 views ### Genetic Algorithm: Need some clarification on selection and what to do when crossover doesn't happen I'm writing a genetic algorithm to minimize a function. I have two questions, one in regards to selection and the other with regards to crossover and what to do when it doesn't happen. Here's an ... 0answers 178 views ### Levenberg-Marquardt for root-finding: just square the function? This question might be so obvious and trivial that I'm having a hard time googling it. I have a multivariate root finding problem that I'm trying to solve in C# and the library that I'm trying to use ... 1answer 57 views ### reduced system: primal-dual interior point method for nonconvex constrained problem When solving a reduced KKT system of a nonlinear (and nonconvex) constrained program after eliminating slack and dual variables, how do we actually take the next step in a primal-dual method? For ... 0answers 16 views ### Procedure to identify characteristic properties of unknown functions in a DAE model I have a system of 1st order odes given by$$ \dot{x_1}(t) = \alpha_1 f_1(x_1,t) + \beta_1 u(t) \\ \dot{x_2}(t) = \alpha_2 f_2(x_2,t) + \beta_2 u(t) $$They are constrained by an algebraic equation ... 0answers 64 views ### overlapping additive schwarz [closed] I am solving 1D laplace problem discretized with finite differences (3-point stencil). I would like to use additive Schwarz method in classical form: U_{k+1}=U_{k}+M^{−1} r_k, where r_k=F−A U_k... 1answer 118 views ### Obtaining a feasible solution for underdetermined system of linear equations satisfying inequality constraints I would like to obtain a feasible solution for an under-determined system of linear equations,$$Ax=b$$where,$A \in \mathbb{R}^{7\times9}, \, x \in \mathbb{R}^{9\times1}\text{and } b\in\mathbb{R}^...
I believe this would be an interesting problem. I have a blackbox function which can take 2-60 input variables $(X_1,X_2,...X_n)$ which are to be optimized. I'm calling this objective function as a ...