> ## Documentation Index
> Fetch the complete documentation index at: https://docs.fincept.in/llms.txt
> Use this file to discover all available pages before exploring further.

# Critical line algorithm

> Markowitz's critical line algorithm: the exact mean-variance frontier under per-asset bounds through its turning points, the max-Sharpe and min-volatility portfolios and the frontier curve.

Toolset `pfopt_cla`: 1 tool.

| Tool | What it does | Notes |
| - | - | - |
| `pfopt_cla` | The critical line algorithm: solves the bounded, fully invested mean-variance problem exactly, returning every turning point (corner portfolio) with its return, volatility and weights, the frontier curve between them (series + line chart), and the max-Sharpe or min-volatility weights with their performance. | |

Inputs, limits and outputs are described in [Fincept Portfolio Optimizer](/guides/fincept-portfolio-optimizer). Full schemas: `fincept_describe_tool`.


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