This tag is intended for questions on methods for the (constrained or unconstrained) minimization or maximization of functions.
3
votes
1answer
75 views
How does fmincon in MATLAB calculate gradients?
I am trying to solve numerically a constrained optimisation problem in MATLAB, and I am wondering how the fmincon function calculates gradients when one isn't ...
1
vote
1answer
34 views
What is a good way to select a small subset (say 50) of items from a large pool of items (say 5 million) while minimizing an objective function?
I have 5 million items that have 10 features (all continuous and not categorical) each and would like to select a small subset of these items. Ideally, I want to manually specify 10 features of my own ...
0
votes
1answer
63 views
Simulation-based Optimization vs PDE-constrained Optimization
What is the difference between Simulation-based Optimization and PDE-constrained Optimization?
Would studying a text on Simulation-based optimization be sufficient to understand and apply both?
1
vote
0answers
36 views
Artificial Neural Network for nonconvex optimization
I want to use artificial neural network(ANN) for solving non-convex optimisation problems. How do I map the constraints and the objective functions in the ANN architecture?
3
votes
1answer
53 views
What is a “good enough” method of assigning values to n variables subject to basic bounding constraints while maintaining relative weights?
Given triples of $n$ floating point values
$$(\min_1, \max_1, w_1), \dots, (\min_n, \max_n, w_n)$$
and a value $V$, what is a good algorithhm to assign values $v_i$ to each of the triples such that ...
2
votes
1answer
110 views
Can the Power Method be used here?
Given a set of $n$ points on which a triangulation is performed, it is possible to construct coefficients $\lambda_{ij}>0$ such that each point $x_i$ is a convex combination of the points connected ...
0
votes
0answers
37 views
Finding attribution of coefficient in a matrix
I have the following $d*n$ matrix in $\{0, 1\}$
\begin{bmatrix}
x_{11} & x_{12} & x_{13} & \dots & x_{1n} \\
x_{21} & x_{22} & x_{23} & \dots & x_{2n} \\
...
4
votes
0answers
73 views
What Derivative-free optimization method should I use when my initial guess is very good?
I am trying to minimize a function where my initial guess is quite close to the minimum.
I'm trying to minimize
$$f(q) = \text{angle}(qw_1q*, v_1) + \text{angle}(qw_2q*, v_2) + \text{angle}(qw_3q*, ...
5
votes
0answers
49 views
conjugate gradient for Newton's method with non positive definite Hessian matrix
I want to minimize a non-linear function $f(x)$ using Newton's method. At each optimization step, I compute a descent direction $d$ to update $x$ using a second-order approximation of $f(x)$:
$$ \...
3
votes
0answers
71 views
Inconsistency in optimize.minimize
I am trying to fit a time-dependent curve at each time step. I do so in minimizing along $x_c$ the quadratic error between the curve and a reference solution $ 1/(1 + \exp\left(\sqrt{S}(x-x_c)\right) $...
3
votes
1answer
32 views
Software for finding a minimum vertex cover for a hypergraph
A hypergraph $H = (V,E)$ consists of a finite set of vertices, say $V=\{1, \dots, n\}$ and a set of hyperedges $E \subseteq \mathcal{P}(V)$. We call $H$ a $k$-hypergraph if all $|e| = k$ for all $e\in ...
0
votes
0answers
39 views
Metric selection and scale-based preconditioning in quadratic optimization problem
I'm going to use scale-based preconditioning in a quadratic optimization problem: minimize $ x^T Q x + p^T x$ such that $ A x + b = 0$ and $D x + E \leq 0$, I want to speed up finding the optimal $x$ (...
0
votes
0answers
27 views
Converting logit coefficients into probabilities through the inverse multinomial logit
I am trying to come up with the transition intensities of a parameterized Markov model, i.e, the elements of the transition matrix weighted by the covariates through the inverse Logit relation:
$$\...
5
votes
1answer
114 views
Generate approximately semi-orthogonal tall matrix approximately satisfying constraints
I have a set of matrices $\{(A_i,D_i)\}$ for $i\in\{1,\ldots,n\}$, where:
Each $D_j\in\mathbb{R}^{S\times S}$ is diagonal, and every entry on the main diagonal is non-negative.
Each $A_j\in\mathbb{R}^...
5
votes
1answer
71 views
Solvers for Quadratically Constrained Quadratic Programs (QCQP) with complex variables
I'd like to know whether there are any publicly available tools for solving QCQP with complex variables (and constraints therefore expressed through Hermitian matrices). What I have found so far is ...
4
votes
1answer
180 views
How to solve the following Frobenius norm-minimization problem?
Background
We know how to solve the following minimization problem
$$
\min_{X} \lVert AX - B \rVert_F^2
$$
But what about the extended version?
$$
\min_{X} \lVert A
\begin{bmatrix}
X & X^2
\...
3
votes
1answer
168 views
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 ...
1
vote
1answer
169 views
How to use CSDP to express a semidefinite program?
I am trying to use CSDP and am struggling with it. Consider, for example, the following semidefinite program
$$\begin{array}{ll} \text{minimize} & 0\\ \text{subject to} & Q - A' Q A - \...
1
vote
1answer
68 views
FMINCON Step Size Tolerance
I get following error after implementing the attached code.
Error Message
"fmincon stopped because the size of the current step is less than
the default value of the step size tolerance but ...
1
vote
0answers
102 views
How to prevent BFGS from getting stuck on astronomically large gradient?
I have implemented BFGS myself from scratch in order to solve minimization problems. Part of BFGS, as I understand it, is that the approximation to the Hessian is supposed to be positive definite, ...
1
vote
0answers
31 views
Best Possible Convex bounds for optimization problems
Suppose we have a primal problem
$$
p^{*}=\min_x f(x), \\\text{s.t.}~~ h_i(x) \leq 0,
$$
where $f(.)$ and $h_i(.)$ are possibly non-convex.
Then its Lagrangian is
$$\mathcal{L}(x,z_i)= f(x) + \...
1
vote
0answers
57 views
Nonlinear least square optimization
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) \...
1
vote
0answers
38 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 ...
0
votes
0answers
40 views
Optimization of a continuous function
This is more like an optimization problem but any solution is appreciated.
I have a data set with input specifying power(demand) to be generated for a particular time period(TP).
Input:
Time --- ...
1
vote
1answer
54 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(...
0
votes
1answer
78 views
ill-conditioning
I am struggling with following exercise from book of Nocedal, Numerical optimization, chapter 2, excercise 2.12:
Suppose that a function $f$ of two variables is poorly scaled at the solution $x^*$. ...
3
votes
2answers
129 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 ...
0
votes
1answer
77 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 ...
0
votes
1answer
43 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 ...
0
votes
0answers
45 views
Methods for Parameter Scaling in Gradient-based Optimization
I am trying to minimize an objective function with 4 parameters, e.g., $a,b,c,d$ using gradient descent. $a < 0.1$, while $0 <b,c,d < 10$.
I'm using a learning rate for all parameters on the ...
6
votes
1answer
198 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 ...
1
vote
1answer
40 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 ...
0
votes
1answer
258 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. ...
0
votes
0answers
50 views
Clarifying a dual problem solution
I’m referring to this question on MathSE about the sum of $k$ largest eigenvalues of a symmetric matrix as an SDP-problem.
I want to solve the maximization problem. As the dual problem is always ...
3
votes
1answer
102 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$$
An equivalent problem is to solve the Euler equation for this functional as a differential equation. ...
1
vote
1answer
39 views
Distribute sources among destinations
There are $n$ sources with the following positive volumes: $p_1, ..., p_n$ and there are $m$ destinations with the following positive volumes: $q_1, ..., q_m$. It is known that $p_1+ ...+ p_n=q_1+ ...+...
7
votes
3answers
441 views
Finding the first N roots of transcendental equation
I need to find the first $n$ roots of the transcendental equation
\begin{equation}
F(k) = J_m'(kr)Y_m'(k)-J'_m(k)Y'_m(kr)
\end{equation}
for integer values of $m$ and any $r \in [0,1)$ where $J'$ ...
0
votes
1answer
104 views
Defining a soft constraint in cvxpy
I am using cvxpy to do a simple portfolio optimization.
I implemented the following dummy code
...
4
votes
1answer
102 views
Nonlinear least-squares solvers vs. generic minimization
A nonlinear least-squares problem with $F:\mathbb{R}^m\to\mathbb{R}^n$,
$$
F(x) \to \min_x \quad (\text{in the least-squares sense})
$$
really means minimizing
$$
\frac{1}{2} \|F(x)\|^2 \to \min_x.
$$
...
2
votes
1answer
90 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 ...
1
vote
0answers
12 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 ...
5
votes
2answers
127 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
votes
1answer
94 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 ...
0
votes
1answer
153 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 ...
0
votes
1answer
106 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 ...
1
vote
0answers
37 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 ...
1
vote
0answers
70 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 ...
0
votes
1answer
54 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 ...
1
vote
0answers
11 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
...
1
vote
0answers
52 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 $r_k=F−A U_k$...
