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To see this, note that the two constraints x 1 (x 1 − 1) ≤ 0 and x 1 (x 1 − 1) ≥ 0 are equivalent to the constraint x 1 (x 1 − 1) = 0, which is in turn equivalent to the constraint x 1 ∈ {0, 1}. Hence, any 0–1 integer program (in which all variables have to be either 0 or 1) can be formulated as a quadratically constrained ...
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Quadratic programming (QP) is the process of solving certain mathematical optimization problems involving quadratic functions. Specifically, one seeks to optimize (minimize or maximize) a multivariate quadratic function subject to linear constraints on the variables.
Convex quadratically constrained quadratic programs can also be formulated as SOCPs by reformulating the objective function as a constraint. [4] Semidefinite programming subsumes SOCPs as the SOCP constraints can be written as linear matrix inequalities (LMI) and can be reformulated as an instance of semidefinite program. [4]
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Linear complementarity, linear and nonlinear programming. Sigma Series in Applied Mathematics. Vol. 3. Berlin: Heldermann Verlag. ISBN 978-3-88538-403-8. MR 0949214. Updated and free PDF version at Katta G. Murty's website. Archived from the original on 2010-04-01. Taylor, Joshua Adam (2015). Convex Optimization of Power Systems. Cambridge ...
An interior point method was discovered by Soviet mathematician I. I. Dikin in 1967. [1] The method was reinvented in the U.S. in the mid-1980s. In 1984, Narendra Karmarkar developed a method for linear programming called Karmarkar's algorithm, [2] which runs in provably polynomial time (() operations on L-bit numbers, where n is the number of variables and constants), and is also very ...
Consider the problem of Linearly Constrained Convex Quadratic Programming. Under reasonable assumptions (the problem is feasible, the system of constraints is regular at every point, and the quadratic objective is strongly convex), the active-set method terminates after finitely many steps, and yields a global solution to the problem.