Linear Programming - Interior-point methodPublic Deposited
Interior point methods are a type of algorithm that are used in solving both linear and nonlinear convex optimization problems that contain inequalities as constraints. The LP Interior-Point method relies on having a linear programming model with the objective function and all constraints being continuous and twice continuously differentiable. In general, a problem is assumed to be strictly feasible, and will have a dual optimal that will satisfy Karush-Kuhn-Tucker (KKT) constraints described below. The problem is solved (assuming there IS a solution) either by iteratively solving for KKT conditions or to the original problem with equality instead of inequality constraints, and then applying Newton's method to these conditions.
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