/**
 * @file src/tableau/simplex.ts
 * @description Simplex algorithm implementation
 *
 * Implements the two-phase simplex method for solving linear programs:
 * - Phase 1: Find an initial basic feasible solution (or prove infeasibility)
 * - Phase 2: Optimize the objective function (or prove unboundedness)
 *
 * Functions are designed to be bound to a Tableau instance via `this`.
 * Uses partial pricing for large problems to improve performance.
 */
import type Tableau from "./tableau";
export declare function simplex(this: Tableau): Tableau;
/**
 * Dual simplex algorithm for warm-starting after adding constraints.
 *
 * Use when: The current solution is dual feasible (reduced costs valid) but
 * may be primal infeasible (some RHS values negative). This is common after
 * adding bound constraints in branch-and-cut.
 *
 * Algorithm:
 * 1. Find a basic variable with negative value (leaving variable)
 * 2. Find entering variable using dual ratio test
 * 3. Pivot to restore primal feasibility
 * 4. Repeat until all basic variables are non-negative
 *
 * @returns Number of iterations, or -1 if dual infeasible
 */
export declare function dualSimplex(this: Tableau): number;
export declare function phase1(this: Tableau): number;
export declare function phase2(this: Tableau): number;
export declare function pivot(this: Tableau, pivotRowIndex: number, pivotColumnIndex: number): void;
export declare function checkForCycles(this: Tableau, varIndexes: Array<[number, number]>): number[];