# Tag Info

Accepted

### Why isn't $x_2+x_3+x_4\le 2$ a cutting plane?

It is a cutting plane, but it is implied by $x_2+x_4\le 1$ and $x_3\le 1$ so not very useful.

### Julia JuMP successive optimization

Your question has a two-part answer: how JuMP handles successive solves, and how the solvers handle successive solves. How JuMP handles successive solves Recall that JuMP is a modeling layer, not an ...

### Objective Integrality Cuts

I am not familiar with objective integrality cuts, but I know that CPLEX has the option to set the parameter absolute objective difference cutoff. If you set this parameter to 1, CPLEX will terminate ...

### Improving cuts from sub-problem with problem-specific hierarchical information

The implied cuts may not be worth adding. Depending on how the solution process goes (solving the master to "optimality" each time before solving the subproblem, versus a "one tree" approach), it ...
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### Family of hard instances for Gomory's cutting plane algorithm

Is there a variant of integer programs for which Gomory's cutting plane algorithm demonstrably takes a superpolynomial number of iterations? Yes Definitions: "Superpolynomial time An algorithm ...
Accepted

### Cutting-planes application procedure for a specific problem

If $|P|$ is not too large, you could try an integer programming formulation. Fix an integer $N>1$ (which will control the granularity of the approximation) and let $\Delta=\frac{H^+ - H^-}{N}$. For ...

### Objective Integrality Cuts

AFAIK Lindo have implemented objective integrality cuts, but I don't know the details of the implementation. It's always a trade-off that depends on what type of problems a solver's users solve more ...

### Julia JuMP successive optimization

I am not familiar with Julia, but you can search for callback and lazycut which allows you ...

### Exploiting ordering to removing infeasible solutions in MILP

Depending on the solver used, you may be able to prioritize the $x$ variables so that variables with higher indices are branched on before variables with lower indices (and elements of $x$ are ...

### How to redefine separation procedure to get 0-1 knapsack with odd number of items

Unfortunately, I also do not know how to embed 0-1-knapsack specific inequalities with the odd number solution requirement. However, I know how to generate cuts that will reduce the search space ...

### Separating violated cover inequalities

A partial answer to part (ii) of your question (this was too long for a comment so I'm including it as an answer). Note that the following assumes a minimal cover. The sequence independent lifting ...
Accepted

### Separating violated cover inequalities

As a heuristic for finding a minimal violated cover inequality, you can solve your min-knapsack problem to find a cover $C$. Then, you may note that all objective function coefficients of the ...
Accepted

### general approach to iterating extreme rays of solution cone

The cone you are describing is often referred to as a basis cone (for instance, in Sec 2.3 of this paper, where the concept is used to derive cuts too). Note that you have such a cone for every ...
Accepted

### Cplex : The cutting stock problem

I think you have some errors when you wrote Cutting method and falls using 2m -200cm- steel bar The model is small enough for a naïve model without pattern: ...