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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
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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
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5
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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…
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
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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
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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
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