This tag is intended for questions on methods for the (constrained or unconstrained) minimization or maximization of functions.
8
votes
2answers
75 views
Genetic algorithm vs conjugate gradient method
I am trying to optimize some force-field parameters in a molecular framework so that the result of simulation comes as close as it can to the experimental structure.
In the past, I have written a ...
-2
votes
0answers
24 views
Stepsize scheme foroptimizing penalty function method [closed]
ii was told to work on various stepsize schemes for optimizing penalty function method. But i got confused on what to do
2
votes
0answers
24 views
Benchmarks or generic configurations for optimal flow control
I am about to test my algorithms for solving optimal control problems of type:
Find an input $u$, such that for a time interval $(0,T]$ the cost functional
$$J(v,u) = \mathcal M(v(T)) + ...
3
votes
2answers
46 views
Trajectory Planning: Polynomials as universal, integrable approximation functions?
I'd like to program a trajectory planner, let's say for a robot, and I can pass acceleration commands to the robot, the robot can move in one dimension. The outcome of the planner is now a vector with ...
3
votes
1answer
55 views
Compute spatial second derivatives in Isogeometric analysis
Motivation:
In isogeometric analysis, state variables(e.g. displacement) are defined in the parametric domain, which can be mapped to the physical domain by $\boldsymbol{\xi}\mapsto \boldsymbol{x}$ ...
1
vote
0answers
30 views
Finite Element, NASTRAN, DMAP, how to print the differential stiffness matrix in .f06 output file
We are working on an optimization problem in which we can approximate the eigenvalue calculation by assuming a constant eigenvector, using the formula:
$$
...
4
votes
2answers
73 views
Optimization algorithm selection for 3 variable integer
I have a cost function: $f(x,y,z) \rightarrow \mathbb{R}$
it is very expensive to evaluate
$x,y,z \in \mathbb{Z}$
0 < x < 10
0 < y < 30
0 < z < 100
I thought it was convex, not ...
3
votes
2answers
113 views
Quadratic Programming: Quadprog
Given a real-rectangular matrix $S$ and inorder to solve this simple quadratic programming problem:
Minimize $w'S'Sw = ||S w||^2$ over $w$ subject to
$e^Tw = 1$ and $w \geq 0$
using a solver I ...
2
votes
0answers
49 views
How much better a bounded BFGS is compared to augmented Lagrangian method with BFGS?
I mean, in handling boxed constraints?
In terms of stability, and more importantly, the numerical performance?
I have already written some well-optimized and well-tested C/CUDA/C++ codes for ...
0
votes
1answer
83 views
Issues with solving large sparse linear equations
I have some issues solving sparse linear equations Ax = b
My matrix A is sparse with dimension of 5 million by 5 million. Actually, it is a combination of two matrices. One is tridiagonal and the ...
3
votes
0answers
65 views
Reformulation of a Frobenius norm maximization problem
This question is extended from this question
The original problem is to maximize the Frobenius norm of a matrix product
$max_{X\in \mathbb{D}}||B^TXA ||_F$, where $\mathbb{D}$ is the doubly ...
7
votes
0answers
74 views
Solving unconstrained nonlinear optimzation problems on GPU
I am trying to solve some unconstrained nonlinear optimzation problems on GPU(CUDA).
The objective function is a smooth nonlinear function, and its gradient is relatively cheap to compute ...
3
votes
2answers
82 views
how can a 2-d fft be constructed to an equivalent matrix?
When I use the cvx matlab toolbox, I met a puzzled problem. The function of fft (or dct, wavelet, etc.) cannot be recognized by the type of 'cvx'. For the 1-d fft, it can be constructed to an ...
0
votes
0answers
15 views
Generating topology (angles and dihedrals) from bond connectivity
Is there a tool out there that will take a file of atomic coordinates or bond connections and generate an output file with the angle (bending) and dihedral (torsion) connectivities? It needs to work ...
3
votes
1answer
52 views
Fitting one set of points to another by a rigid motion
I'm not really sure how to explain this problem clearly, so please bear with me.
I have a basis of 3 orthonormal unit vectors and a position, a standard 4x4 transform matrix in computer graphics.
...
1
vote
2answers
65 views
Topics for project
I was assigned a project in my intro to computer programming class. The goal is to implement a numerical model to some engineering or physics/science problem. The course uses Java.
eg. soccer ball ...
1
vote
1answer
45 views
Dakota Optimizer - plot objective functions in real-time
I am using the Dakota Optimizer.
I have 50+ variables, 50+ constraints and more than one objective function.
Independent of the actual optimizer used, or the output selected:
Is there a way to plot ...
8
votes
3answers
172 views
Fortran: Best way to time sections of your code?
Sometimes while optimizing code it is required to time certain portions of the code, I have been using the following for years but was wondering if there is a simpler/better way to do it?
...
0
votes
2answers
53 views
Analytical form of the minimum of a function with absolute values
I would like to find the analytical form of the point which minimizes the following function:
$$
f(x_T) = \frac{1}{T} a_1 (x_T-x_0)^2 + a_2 |x_T-x_0| + T a_3 + \sum_{i=1}^M p_i \left[b_{1i} (x_T - ...
2
votes
2answers
84 views
Differences between “least square”, “mean square” and “least mean square”?
I was wondering what differences are between the terminology: "least square (LS)" "mean square (MS)" and "least mean square (LMS)"?
I get confused when reading in Spall's Introduction to Stochastic ...
3
votes
1answer
82 views
Optimize an unknown function which can be evaluated only?
Given an unknown function $f:\mathbb R^d \to \mathbb R$, we can evaluate its value at any point in its domain, but we don't have its expression. In other words, $f$ is like a black box to us.
What is ...
5
votes
2answers
120 views
Which is easier to solve, regularized minimization, or constrained minimization?
Following regularized minimization problem
$$\min f(x) + \lambda g(x)$$
where $\lambda>0$,
and following constrained minimization problem
$$
\min f(x)
$$
s.t.
$$
g(x) \leq \epsilon
$$
where ...
8
votes
3answers
179 views
Confusion about compressed sensing problem
I read some references including http://en.wikipedia.org/wiki/Compressed_sensing.
I am kind of confused what optimization problem compressed sensing builds and tries to solve. Is it
$$ \min_x ...
0
votes
1answer
64 views
Unique Partition of a Graph
Given an undirected graph, is it possible to find a criteria that leads to a unique partition of the nodes? The graph is not weighted.
2
votes
1answer
46 views
Cplex C++ Interface: How to add many constraints quickly?
I noticed that adding constraints to an IloModel one by one can be prohibitively slow. (I am referring to the construction of the model, not the optimization.)
...
5
votes
3answers
105 views
Closest interior point on integer grid to a vertex of a convex polyhedron
I have a 3 dimensional convex polyhedron whose vertex coordinates are rational. For one of these vertices, I would like to find the nearest integer grid point (under the Euclidean metric) that is ...
2
votes
2answers
71 views
Maximizing distance between point particles
I have a situation where I am trying to maximize the distance between some point particles. For example, I have a periodic simulation box that is 100 Å$^3$, and I am putting in 361 particles. ...
3
votes
1answer
38 views
Do the ellipsoid methods belong to the trust region methods?
Do the ellipsoid methods belong to the trust region methods?
Reading their descriptions I tend to think the idea of the ellipsoid methods belong to the idea of the trust region methods, but am not ...
2
votes
2answers
85 views
Are these two formulations of semidefinite programming problems equivalent?
From Wikipedia
Denote by $\mathbb{S}^n$ the space of all $n \times n$ real symmetric matrices. The space is equipped with the inner product (where ${\rm tr}$ denotes the trace) $$\langle ...
4
votes
1answer
129 views
What is a vector programming problem?
In a note:
semi-definite programming is equivalent to vector programming.
...
A Vector Program is a Linear Program over dot products.
In Boyd's Convex Optimization, a vector ...
6
votes
1answer
82 views
Least absolute deviations solving using the Barrodale-Roberts-algorithm: Premature termination?
Please excuse the longish question, it just needs some explanation to get down to the actual problem. Those familiar with the mentioned algorithms probably could jump directly to the first simplex ...
4
votes
1answer
82 views
Confusion related to convexity and concavity of a function
I was reading this paper http://www.ist.temple.edu/~vucetic/documents/wang11kdd.pdf related to adaptive multi-hyperplane machine for non linear classification
In that paper, they have mentioned about ...
3
votes
1answer
106 views
Confusion about Armijo rule
I have this confusion about Armijo rule used in line search. I was reading back tracking line search but didn't get what this Armijo rule is all about. Can anyone elaborate what Armijo rule is? The ...
6
votes
2answers
80 views
Confusion related to convex optimization
I have been reading about convex optimization. We have:
minimize $f(x)$ s.t. $h(x) = 0$, $g(x) \le 0$, $x \in X$
It's Lagrangian dual is:
maximize $\phi(\lambda,\mu)$ s.t. $\mu \ge 0$, where ...
5
votes
1answer
142 views
What is the correct formulation of this problem, and how can I solve it efficiently
I'm looking at finding a solution to the following problem, but I'm having trouble formulating it sensibly, and then finding an appropriate algorithm to solve it.
Consider a list of items placed in a ...
8
votes
1answer
76 views
large dense low rank assignment problem
Is there a reasonably cheap method to solve the large, dense, low rank assignment problem $\max_\pi \sum_i A_{\pi i,i}$, where $\pi$ runs over all permutations.of $1:n$?
Here $A$ is an $n\times n$ ...
0
votes
0answers
31 views
Robust Counterpart of an uncertain LP
Consider the following robust optimization problem:
min c'x
s.t.: $Ax\geq b \;\;\forall (A,b)\in \mathcal{U}$.
Why can the robust counterpart of the problem be written in this form?
$min_x{\{ ...
2
votes
0answers
53 views
Algorithm to distribute symbols uniformly in a square grid?
Given a square grid of size $n\times n$ and $m$ symbols (say for example, alphabets A, B, C...), having $N(i)$ number of $i$th symbol; $\sum_{i=1}^{m}N(i) = n\times n$. Is there any computationally ...
3
votes
1answer
76 views
Algorithm for dealing with medium-size non-convex QCQP
I have the following problem:
$$\displaystyle\min_{x}x^HAx$$
subject to constraints:
$$x^HBx = 1$$
$$x^HC_ix = 0$$ for $i$ = 0,1,...,203.
$x$ is complex and 205x1.
$A$ and $B$ are complex 205x205 ...
1
vote
1answer
56 views
nonlinear programming with support constraint
I want to solve a nonlinear optimization problem
$$\underset{\mathbf{x}\in \mathbb{R}^n}{\operatorname{argmin}} f(\mathbf{x})$$
subject to a support constraint $$\mathbf{x}=[x_1,\cdots,x_n]^T, \quad ...
2
votes
0answers
52 views
What are Implications of Commutative Diagrams?
This question may be too broad. But I really want to know some concrete explanations. I often find various commutations appear here and there, which concerns the application order of two operators. ...
0
votes
1answer
27 views
Polynomial solvability [duplicate]
Consider the following optimization problem:
Min$_{x}$ $\qquad \sum_{(i,j,t,s)\in I_r}||x_ix_j-x_tx_s||^2$
S.t.: $\qquad x\in \mathcal{C} ;$
where $x=(x_1,x_2,...x_n)$
and $\quad x_j\geq 0\;\; ...
1
vote
1answer
49 views
Feasibility checking
Consider the following optimization problem:
$Min\;\;\; CX$
$AX\geq b$
$x_ix_j= x_s x_t\;\;\; i\neq j \neq s\neq t$
$x_j\geq 0;$
Where $A$ is the adjacency matrix and $C$ is a constant vector.
...
2
votes
1answer
73 views
polynomial time solvability
Consider the following optimization problem:
$Min \qquad C^TX$
S.t.: $\qquad AX=0;$
$x_ix_j=x_kx_t$$\quad $for some $i\neq j\neq k\neq t$
$X=(x_1,x_2,...x_n)$
and $\quad x_j\geq 0\;\; ...
0
votes
1answer
107 views
Semidefinite programming
I have a convex optimization problem that is essentially a linear objective function over some linear constraints and also a semidefinite matrix in the following form: $
M=
\left[ ...
5
votes
2answers
99 views
minimization problem: sum of Rayleigh quotients
I would like to find $x$ which minimizes the following equation:
$\frac{x^HAx}{x^HBx} + \frac{x^HCx}{x^HDx}$ where A, B, C, D are positive-definite. $x$ is not a very large vector (<1000 elements ...
4
votes
1answer
69 views
Algorithm to find singularities of a log function
I have a numerical problem in which I need to find the values $\lambda$ for which the determinant of a matrix $A_\lambda$ is zero. (The solutions $\lambda$ will give the eigenvalues of an operator...)
...
2
votes
1answer
64 views
Nonlinear bad constraints
I have an optimization problem with linear objective function. The constraints are in two different groups. The first set of constraints are linear while the second set is nonlinear. The nonlinear ...
2
votes
0answers
25 views
A cost function minimisation genetic algorithm which includes a measure of search completeness?
I am looking at ways of finding the global best-fitting model to a set of data. The model is highly non-linear and has anywhere between 5 and 8 parameters.
I have used particle swarm optimisation ...
4
votes
1answer
97 views
Conway's FRACTRAN
I've implemented fractran and playing with sequences iteratively in C.
http://mathworld.wolfram.com/FRACTRAN.html
Sloan: http://oeis.org/A007542
I can generate correct results, but I would like to ...
