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Results tagged with global-optimization
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user 9022
7
votes
Accepted
Nonlinearly constrained optimization (quadratic)
The real issue here is the constraint
$\sum_{i} x_{i}1_{x_{i}>a} < b $
whose left hand side has horrible discontinuities.
Rather than using a solver designed for problems with continuous variable …
- 3,934
6
votes
Computational complexity of unconstrained convex optimisation
Some books to start with for background reading would include:
Y. Nesterov, Introductory Lectures on Convex Optimization: A Basic Course, Springer, 2003.
Y. Nesterov and A. Nemirovsky, Interior Poin …
- 3,934
6
votes
Accepted
Optimizing a quadratic restricted to the sphere
Your problem has been studied extensively in the context of trust region methods for optimization, and there are a number of algorithms that have been developed.
See for example:
W. W. Hager, Mini …
- 3,934
4
votes
Accepted
Linear program to maximize the minimum absolute value of linear functions ?
Unfortunately, this problem can't be represented by an LP, since your feasible region is in general nonconvex, and the feasible region of an LP (being the intersection of a bunch of half spaces) is al …
- 3,934
3
votes
Accepted
Maximizing the minimum of piecewise linear functions in high dimensional space
As in your previous question, this is a nonconvex optimization problem, so it won't be LP, SOCP, or SDP representable.
You've only got a 21 dimensional problem, and the constraint functions have ea …
- 3,934
2
votes
Robust black box function minimization with extremely expensive cost function
You haven't said so explicitly, but it sounds as though your function evaluations may also be noisy in that the function value is the result of a Monte Carlo simulation that incorporates random number …
- 3,934
1
vote
Efficient Algorithm For Projection Onto A Convex Set
You haven't told us anything about the size of your problem instances. How many terms are there in the sum of norms? What is $n$?
Your problem is an example of a "sum of norms" optimization probl …
- 3,934
1
vote
Optimal knot placement for fitting piecewise-continuous linear functions to a nonlinear func...
Do you really want to solve this problem, or do you just want to get a good approximation to the function? I would bet that your overall goal is actually to get a fast and reasonably accurate approxi …
- 3,934
1
vote
QUBO formulation of a discrete-variable Genetic Algorithm optimization problem
The binary encoding trick requires you to actually bound the $N$ parameters. Suppose that $m$ bits suffice for each of the $N$ parameters. Then you have $L=2^{mN}$ bits in your QUBO. Even then, you …
- 3,934
0
votes
Efficient algorithm for finding the minima of a piecewise linear function
The problem
$
\min_{x} \max_{i} a_{i}+b_{i}x
$
(It doesn't really matter whether $x$ is a scalar or a vector) can be formulated and solved as a linear programming problem
$
\min_{x,t} t
$
$
…
- 3,934