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1500 questions
5
votes
1 answer
Minimize sum of ReLU
I am trying to minimize a function of the following form
$$f(\vec{x}) = \sum_{i = 1}^n\operatorname{ReLU}(\vec{v}_i \cdot \vec{x} + b_i) $$
$x \in \mathbb{R}^m$ with $m$ around $100$ to $1000$ and $n$ around $10^5$ to $10^7$. I wish to get to the…
JEK
- 121
- 2
5
votes
2 answers
Book to learn metaheuristics
I want to learn about metaheuristics and start building one to solve combinatorial optimization which is pretty hard to solve. I am looking for book recommendation or any learning experience to learn this topic. Python preferred for the programming…
overboxed
- 593
- 1
- 12
5
votes
2 answers
Minimizing under argmin constraint
I have a problem in the form
$$\begin{aligned}
\min_a f(a,b)\\
\text{s.t.}\ b =\ & \arg\min_c g(a,c)\\
& \text{s.t.}\ H(a,c) \leq \vec{0}
\end{aligned}$$
where $f, g, H$ are all linear functions. Actually, if there are multiple $c$ such…
Arktus
- 51
- 1
5
votes
2 answers
Transform nonlinear cost function to get LP or MILP
I'm trying to schedule power of multiple prosumers in a microgrid.
The problem includes a cost function with min and max statements since I want to distinguish between the prices for importing and exporting energy.
The following is a minimal example…
Daniel Stich
- 153
- 4
5
votes
1 answer
Changing a parameter while branching in SCIP
I use pyscipopt. I know how to add constraints while branching using handlers (kind of), but now I want also to change some parameters. I imagine is similar, but couldn’t found an example.
What I want is as follows:
-Every time a feasible node is…
orpanter
- 517
- 3
- 10
5
votes
1 answer
Additional resources for this type of problem formulation
I'm working on a problem with the following formulation:
\begin{align}
\min&\quad\sum_{i \in N} \sum_{j \in J} V_{ij}x_{ij}
\\
\text{s.t.}&\quad \sum_j x_{ij} = 1 \quad \forall i \in N\\
&\quad V_{ij} = \sum_{k \in N(i)} C_kx_{kj} \quad \forall i…
Bob Jeans
- 93
- 3
5
votes
1 answer
Use of variance in job ordering
For a job-shop-like problem I have some constraints of this form:
$$
c_i \geq s_i + d_{iom} z_{iom}
$$
$z_{iom}$ is a binary enabler, $d_{iom}$ is the delay on job $i$ for operation $o$ done by machine $m$, $s_i$ is the start time, $c_i$ the…
Brannon
- 900
- 2
- 12
5
votes
2 answers
Analyzing the output of IPOPT
I am solving a feasibility (No objective) problem in IPOPT. I got the following output:
I see that the violation of the constraints are of order 1e-15. What is the meaning of dual infeasibility 1e-07 and the overall NLP error 2e-09? I mean what do…
Rudinberry
- 191
- 5
5
votes
0 answers
Scale of largest CPLEX/Gurobi execution
I am trying to understand the CO2 emission of large scale optimization using CPLEX or Gurobi. Is there a published literature which addresses the compute usage of large scale executions?
Omar Shehab
- 251
- 1
- 3
5
votes
0 answers
Reduce overhead Gurobi Python getting and setting attributes
I am using Gurobi 9.5.1 in Python 3.10. In the context of column generation I request the duals of the master problem and set them in the objective of the subproblem. This is done repeated times.
duals = master.getAttr(GRB.Attr.Pi,…
rllb
- 51
- 2
5
votes
0 answers
How to overcome overflow issues with Concorde?
Concorde is a well-known exact solver for instances of the traveling salesman problem. It can also be used to solve asymmetric TSPs, if the user implements a trick to convert ATSP to TSP.
However, if the problem size is large enough, the resulting…
Ike348
- 283
- 1
- 5
5
votes
2 answers
Quadratically constrained convex optimization
I have tried to convert the following constraint into SOCP form but can't figure it out. My issue is that whenever I create the norm, the other side has to be square rooted which invalidates the SOCP form.
The directional parameters ${\boldsymbol…
Mosab Qaissiah
- 51
- 1
5
votes
1 answer
Knapsack problem with negative value and weights and cardinality constraint
I know there are ways to handle Knapsack problems with negative weights or cardinality constraints, but I have a problem with also negative values as well as a cardinality constraint:
\begin{align}
\max & \sum_{i\in N} u_i x_i \\
\text{s.t.} &…
Jeffrey
- 53
- 4
5
votes
2 answers
Julia JuMP successive optimization
I am using Julia's JuMP package to solve a cutting-plane method. Namely, I solve a sub-problem, find the most-violated constraint in the master problem, add that to the sub-problem and reoptimize.
My main problem is an exponential cone problem and I…
independentvariable
- 3,980
- 10
- 36
5
votes
3 answers
What is the go-to practical method for optimizing separable quadratic programs?
I have a quadratic program that looks like this:
For fixed vector $b$, and matrices $A_1, ..., A_n$, Find column vectors $x_1, ..., x_n$ that minimize $\sum_{i=1}^n x_i ^T 1 1^T x_i$ subject to $\sum_{i=1}^n A_i x_i = b$ and $x_i\in \mathcal{X_i}$,…
AspiringMat
- 151
- 2