/**
 * @file src/tableau/lu-simplex.ts
 * @description LU-based simplex algorithm
 *
 * Uses LU factorization of the basis matrix instead of explicit row operations.
 * This reduces pivot cost from O(n*m) to approximately O(n²) per pivot,
 * plus O(n) for LU updates.
 *
 * Key differences from standard tableau simplex:
 * - Stores original constraint matrix A, not B^{-1}A
 * - Computes reduced costs via BTRAN
 * - Computes pivot column via FTRAN
 * - Updates LU factors instead of row operations
 */
import type Tableau from "./tableau";
import { LUFactorization } from "./lu-factorization";
/**
 * Run LU-based simplex on the tableau.
 * This modifies the tableau in place and returns it.
 */
export declare function luSimplex(this: Tableau): Tableau;
/**
 * LU-based pivot operation.
 * This is the key optimization - instead of O(n*m) row operations,
 * we update the LU factors in O(n) time.
 */
export declare function luPivot(this: Tableau, lu: LUFactorization, leavingRow: number, enteringColumn: number): void;
/**
 * Check if LU simplex should be used based on problem size.
 * LU overhead is only worthwhile for larger problems.
 */
export declare function shouldUseLU(tableau: Tableau): boolean;