# Questions tagged [feasible-points]

For questions specifically about existence (feasibility), counting feasible points (in a discrete setting), or partitioning the feasible region (e.g. in the context of branch-and-bound methods). Feasible points are those which satisfy all the constraints of a problem, and so can be defined without regard to any optimization criterion.

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### How to correct this scheduling algorithm?

I have a scheduling problem to solve. It's a resource-constrained project scheduling problem with time-varying resource availabilities. The objective is minimizing tardiness. The full detailed model ...
42 views

### Feasible sets represented as point clouds

Does the situation in optimization ever occur in which you have a problem whose feasible set is not described in terms of explicit algebraic equations, but instead you have a large set of points that ...
110 views

### Estimation of the number of optimum vertices

Consider any linear programming model of $n$ variables and $m$ constraints which has multiple optimum solutions. If it is possible, I'd like to know the lower and upper limits (in terms of $n$, $m$ ...
136 views

### Find a point inside non-empty difference of ellipsoids

Given two ellipsoids \begin{align}\mathcal{E}_1 &= \{ X \mid X^\top A_1 X + 2B_1^\top X + C_1 \leq 0\}\\\mathcal{E}_2 &= \{ X \mid X^\top A_2 X + 2 B_2^\top X + C_2 \leq 0\}\end{align} are ...
158 views

### Find all Combinations of a Matrix

I have a $16\times11$ matrix and want to find all eligible* combinations of this matrix including always entities from all 11 columns. A simple example from a $2\times3$ matrix would be the following:...
79 views

### Is there a library of infeasible MINLP problems?

We have a number of test libraries to test solver performance like MINLPLIB, QPLIB, etc., but the problems in all libraries I know are overwhelmingly on the feasible side. Is there a library to test ...
189 views

### When using docplex.cp is it possible to get all feasible solutions?

I would like to solve an ILP and get all feasible solutions (even the worst one). How could I do that using docplex.cp? I've seen a similar question in: Using CPLEX "solution pool" to count ...
116 views

### How can I solve this problem?

I have $N_{\rm C}=8,$ and $N_{\rm U}=25$ Scenario 1: $$\frac{l_{c,u}}{\sum\limits_{c=1}^{N_{\rm C}}l_{c,u}}\ge 0.1,\quad\forall u,u=1,2,\cdots,N_{\rm U}$$ and \sum_{u=1}^{N_{\rm U}}l_{c,u}\le 1,...
1k views

### Why is there not a feasible solution for a MIP?

Is there a way to see why a solver (OR-Tools, CPLEX, Gurobi) cannot find a feasible solution when solving a MIP? By that I mean, is there a possibility to show at which constraint and exact indices ...
2k views

### Find feasible point in polynomial time in linear programming

Background A while ago my team was implementing an interior point LP solver and we came across the following conundrum: Is there a polynomial-time algorithm to find a feasible starting point in ...