Calculator Input
Example Data Table
Use this sample to test the solver. It is already loaded as the default set.
| Objective Type | Objective | Constraint 1 | Constraint 2 | Constraint 3 | Initial Guess | Expected Region |
|---|---|---|---|---|---|---|
| Maximize | 5x + 4y | x + y ≤ 6 | 3x + y ≤ 9 | x + 2y ≤ 8 | (1, 1) | Near (2, 3) |
Formula Used
This page solves a two-variable linear program with strict interior feasibility:
subject to aᵢx + bᵢy ≤ cᵢ, for each active constraint
and x > 0, y > 0
[x, y]ₙₑw = [x, y] + αd
How to Use This Calculator
- Choose maximize or minimize, then enter the objective coefficients for x and y.
- Activate each required constraint and fill the values for a, b, and c in the expression a·x + b·y ≤ c.
- Enter an initial guess, or keep automatic feasible start enabled for safer interior initialization.
- Adjust μ, reduction factor, tolerance, and iteration limits when you want tighter convergence control.
- Click the solve button to generate the result section above the form.
- Review the solution, slack table, convergence graphs, and then export the report as CSV or PDF.
FAQs
1. What type of problem does this solver handle?
It solves two-variable linear programs with active constraints written as a·x + b·y ≤ c, while keeping x and y strictly positive during interior iterations.
2. Why is a feasible starting point necessary?
The logarithmic barrier is only defined inside the feasible region. If any constraint is violated, or x or y is nonpositive, the barrier expression breaks.
3. What does the barrier parameter control?
A larger μ keeps the iterates deeper inside the feasible region. As μ shrinks, the solution moves closer to the true constrained optimum.
4. Why do some constraints show “Near active”?
That label means the final slack is very small. Such constraints are close to binding and usually define the edge of the optimal solution.
5. Can this page solve equality constraints directly?
Not directly. This version is designed for inequality constraints. Equality conditions must be reformulated before using this interface.
6. What does the path chart represent?
It plots the accepted interior iterates in the x-y plane, along with the active constraint boundaries, so you can see how the solver approaches the optimum.
7. Why might the line search stall?
Stalling can happen when the model is ill-scaled, nearly infeasible, or numerically sensitive. Try a different feasible start, looser tolerance, or fewer extreme coefficients.
8. What should I export: CSV or PDF?
Use CSV when you want raw numeric rows for analysis. Use PDF when you want a shareable snapshot with the summary, tables, and charts.