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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1answer
119 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 $...
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2answers
184 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 ...
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1answer
161 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 ...
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1answer
49 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 ...
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1answer
307 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 ...
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1answer
43 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 ...
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1answer
370 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. ...
3
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1answer
251 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. ...
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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+ ...+...
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3answers
937 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 $J'$ ...
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1answer
650 views

Defining a soft constraint in cvxpy

I am using cvxpy to do a simple portfolio optimization. I implemented the following dummy code ...
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1answer
118 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 $$ \frac{1}{2} \|F(x)\|^2 \to \min_x. $$ ...
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1answer
146 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 ...
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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 ...
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2answers
1k 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 ...
3
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1answer
365 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 ...
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1answer
1k 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 ...
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1answer
190 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 ...
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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 ...
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0answers
203 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 ...
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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 ...
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0answers
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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 ...
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0answers
65 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 $r_k=F−A U_k$...
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1answer
134 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}^...
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1answer
478 views

Optimization of a blackbox function with an equality constraint?

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 ...
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1answer
65 views

Adaptive gradient descent

I want to minimize some multivariable function $\Delta(\alpha, \beta)$. I know that this function has a zero point, $\Delta(5, 5) = 0$. Starting from some $(\alpha, \beta)$ close to $(5,5)$ (e.g. (4....
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1answer
668 views

Ways to speed up solving an LP with Google's ortools

I'm having an issue solving an LP of the form: $$\min z = c^Tx$$ $$\text{s.t.}$$ $$Ax \geq b$$ $$x\geq p$$ $1 \leq a_{ij} \ll b_i$, $p \leq 0$, and $c \geq 0$ The specific problems I'm running into ...
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0answers
102 views

Are the No Free Lunch Theorems Useful for Anything?

I have been thinking about the No Free Lunch (NFL) theorems lately, and I have a question which probably every one who has ever thought of the NFL theorems has also had. I am asking this question here,...
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3answers
173 views

Optimization of a blackbox function

Let's say that we have an objective function $f(\mathbf x,\mathbf y)$ which has the parameters $\mathbf x=[x_1\ldots x_n]$ and $\mathbf y=[y_1\ldots y_n]$. Here, $\mathbf y$ is a blackbox variable ...
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0answers
38 views

Meaning of “points where the first- and second-order optimality conditions fail”

I am reading a paper that summarizes a set of simulations. Basically, the authors are trying to minimize some function using different optimization algorithms. They conclude: "Our findings point to ...
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1answer
75 views

Large-scale almost-linear optimization

I'm currently trying to minimize the following function: $$\min_{\mathbf x,\mathbf y,s} \|F\mathbf x-\mathbf a\|_2^2 + \|SF\mathbf y-\mathbf b\|_2^2 + \lambda \|\max(\mathbf x, \mathbf y)\|_1,$$ $$\...
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0answers
91 views

Sequential Quadratic Programming for Quadratically Constrained Quadratic Programs

A standard Quadratically Constrained Quadratic Program (QCQP) is of the form: $$ \underset{x}{minimize} \frac{1}{2}x^TP_{0}x + q_{0}^{T}x $$ $$ subject \; to \quad \frac{1}{2}x^TP_{i}x + q_{i}^{...
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1answer
95 views

Free access to Xeon Phi clusters

Apologies if this is not the right forum to ask, but there has been a somewhat related question here. I am working on a piece of software (nonlinear constrained optimisation, coded in C++11 and ...
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2answers
78 views

Find combinations of variables with variable bounds to get summed up to a required value (using Python)

Let's say I have n variables. Each variable has lower and upper bounds. I want to find all suitable combinations of these variables to sum up to a required value. An example with two variables: $$ ...
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2answers
349 views

Knapsack problem with fixed number of elements?

I am looking at an optimization problem that looks like this: $$ \text{minimize}\;\; \mathbf{x}^TQ\mathbf x \;\;, \; \mathbf x \in \mathbb R^n, x_i \in \lbrace 0, 1 \rbrace\\ \text{subject to}\;\; ||...
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0answers
74 views

Find a vector B that minimizes |W-A*B|

I want to find a candidate vector $B$ that $$\min|(W - A_i * B_i)|$$ $$ a_i > 0,\ A_i=\{a_0,...,a_i\},\ B_i=\{-1,0,1\}^i$$ For example, given $$W = 0.6,\quad A_4 = [0.1, 0.2, 0.4, 0.7] $$ one ...
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0answers
53 views

Obtaining the lagrangian multipliers in an optimization problem

Suppose we have this simple optimization problem \begin{align*} \underset{x\in V}{\text{min}} &~ f(x) \\ \text{s.t.}& ~x \leq \beta \end{align*} Using slack variables \begin{align*} ...
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0answers
73 views

Nonlinear global optimization algorithm that can use dynamic programming

I've asked this question on stackoverflow 2 weeks ago, but, judging by zero response, that probably was the wrong forum. Therefore copying it here: Let F0,...,Fn ...
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0answers
59 views

BFGS convergence problem

I would like first to state that it is beyond my capability to identify whether this is a BFGS issue or a R package problem. I've been doing some mixed logit regression using the R package "mlogit". ...
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1answer
465 views

Trajectory optimization for smoothness

I want to achieve the following in 2D (and without obstacles): Given start position A and end position B, generate the path between the two points that optimizes a cost function that depends on total ...
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1answer
132 views

pde-constrained optimization

I'm trying to solve a problem where I have a initial and final distribution of tumor, and my goal is to find the best map of parameters (diffusion and reaction terms) for a reaction-diffusion equation,...
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1answer
71 views

Solving for $C$ in $Q = YCZ$ using least squares in Matlab

I am trying to solve for the matrix $C$ in $Q = YCZ$ in matlab. I have preliminary results but they don't seem realistic. Here, $Q$ is $n \times m-1$, $Y$ is $n \times p$, $C$ is $p \times m$ and $Z$ ...
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0answers
52 views

Finding minimum of Wronskian determinant

If I have a partial differentail equation such as $\frac{\partial^2 u}{\partial t^2} + c^2 \frac{\partial^2 u}{\partial x^2}$, with boundary conditions $u(0,t) = 0$ and $u(1,t)=0$, I can solve this ...
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0answers
445 views

Using C/C++ for Markov chain Monte Carlo (MCMC) methods

I'm working on optimizing the parameters of a mathematical model to fit experimental data, using an existing formula for the likelihood of observing the data given a set of parameter values. At the ...
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3answers
289 views

How can I use Projected Gradient Descent for this optimization problem with constraint?

Suppose $ q $ and $ A $ are given and that $ q, p \in R^{N} $ and $ A \in R^{NxN} $, then how can I find the vector $ p $ such that $$ (q - p)^{T}A(q - p) $$ is minimized constraint to $ \sum_{i=1}^{...
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0answers
53 views

Algorithm design to filter on 5,000 stocks each of which has 4 months worth of data points

I want to filter on 5000 stocks, each of which has 4 month or more worth of data (>= 500 data points each). my filtering criteria will be based on 8 calculated values from the data points. for example,...
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1answer
65 views

Why can't we discretize continuous domains in distributed non-convex constraint optimization problems?

Consider a non-convex distributed optimization problem. We have $X$ = a set of $n$ decision variables: $x_i$ where $i=1..n$ and $x_i \in R$, the set of Reals. We have $F$ = a set of $m$ constraint ...
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0answers
160 views

Linear regression with inequality constraint in Java

I haven't been doing math in years and I'm facing the following problem. I'm trying to implement in Java a linear regression under a set of inequality constraints. Sorry in advance for all the ...
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1answer
169 views

Robust/Tested Solver for incompressible 2D Euler (Fluid dynamics) Equation

I am trying to locate suitable computational algorithms for a optimization problem that requires repeated solution of transient 2D incompressible Euler equation on a 2D domain (say rectangular). My ...
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1answer
251 views

Why do active set methods or the simplex method pivot only one variable at a time?

Why do active set methods or the simplex method pivot only one variable at a time? Ostensibly, we could add multiple columns to the basis during pivoting, but the standard presentation of the methods ...

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