Questions tagged [constrained-optimization]
Questions about optimization problems subject to additional constraints.
310 questions
2
votes
1
answer
148
views
Can a Second Order Cone Program (SOCP) be posed in terms of the L1 Norm?
In a Second Order Cone Program (SOCP) the constraint is stated as
$$||Ax - b||_2 \leq c^Tx + d$$
where $|| \cdot ||_2$ is the $L2$ norm.
Can this instead be translated to a problem constrained to
$$||...
- 23
1
vote
0
answers
59
views
References on equality-constrained matrix-free inexact SQP
I want to implement an equality-constrained SQP method for a fairly large and sparse problem. As such I need to use iterative solvers where my matrix-vector products are matrix-free. Also I compute my ...
- 3,021
0
votes
0
answers
78
views
Calculating maximum of a function of several variables using a computer
Consider the function
$$f(r,s,t,a,b)=rst-e^{t^a}-e^{r^b}-s(\ln(s))^{\frac{1}{a}+\frac{1}{b}}$$
where $r$, $t>0$ and $a$, $b$, $s\geq1.$
Is there any software that can calculate approximately the ...
2
votes
0
answers
156
views
Scaling the objective function in a constrained optimization problem
I am trying to minimize a scalar function $f(\bf x)$ while satisfying a vector of constraints ${\bf {c}}({\bf{x}})$. Together, the function and the constraints form the Lagrangian
$$
L({\bf x}, {\bf \...
- 375
2
votes
0
answers
84
views
constrained optimization and active constraints at solution: statistical measures
Suppose we want to minimize an objective function (fitting parameters of a PDE) and the parameters have box constraints and linear inequality constraints. Some of the constraints are active at the ...
1
vote
0
answers
83
views
Dogleg Trust Region Method Fail
I'm implementing in Julia the Dogleg Trust Region Method.
I've got this:
...
2
votes
4
answers
273
views
Maximizing $\operatorname{Tr}(X)$ subject to $XX^T=I$ and $AX=B$ constraints
I have a $n\times n$ matrix $X$ and I'd like to maximize $\operatorname{Tr}(X)$ subject to $XX^T=I$ and $AX=B$ constraints.
Are there any well-known relaxations/methods to deal with this problem?
This ...
- 2,779
9
votes
0
answers
165
views
Compelling demonstrations/examples on ill conditioning of penalty methods
It's known that penalty methods in optimization suffer from ill conditioning. But is there simple yet compelling demonstrations/examples to teach this concept to convince and visualize for learners?
...
- 325
1
vote
1
answer
102
views
Regular constraints
I am going through some exercises in a presentation I found treating the basics of math for machine learning, and they talk about regular constraints.
For example, this set $K = \{(x,y) \in R^2 / x+y =...
- 113
0
votes
1
answer
75
views
Estimating the rate of convergence of Projected Gradient Descent on constrained polynomial objectives
I am estimating the order of convergence of Projected Gradient Descent (GD) on quadratic polynomials with random coefficients independently drawn from Uniform(-1,1) and bounded by a unit hypercube. I'...
- 23
0
votes
1
answer
138
views
Is the NLP formalism sub-optimal for real-world problems
My home-brew optimization studies have raised yet another fundamental question. The Nonlinear Programming formalism, "minimize f(x) subject to inequality and equality constraints, and x ...
- 357
3
votes
0
answers
113
views
Iterative Solvers for Linear Least Squares with Integer Constraints
The classical linear least squares problem reads $\min_{x\in\mathbb{R}^n}\|Ax-b\|^2_2$ and its solutions satisfy the normal equations $A^{\top}Ax = A^{\top}b$. A standard approach to solve the latter ...
- 3,021
0
votes
2
answers
278
views
BFGS Constrained Optimization Failure Due to Precision Loss
I am trying to optimize the following objective function according to some constraints. However, the optimization fails at the first iteration with the message that the desired error was not ...
0
votes
0
answers
50
views
Methods for delaying the "break" in non-linear least squares optimisation when the step size gets too small?
I am using the Levenberg-Marquardt method for calibration purposes. Typically, the RMSE of my calibration looks like:
I want to break the algorithm when the algorithm step-updates start to slow down, ...
1
vote
0
answers
49
views
Constraints involving max in ILP
Consider $n$ apps and $m$ transactions. $x_{ij}$ is a binary variable, it takes 0 or 1. $x_{ij}$ takes 1 if $i$th app is used for $j$th transaction, else 0.
min $\sum_{i=1}^{n}\sum_{j=1}^{m} x_{ij}$
...
- 111