Duality and sensitivity in nonconvex quadratic optimization over an ellipsoid

Article Abstract:

The problem of optimizing a nonconvex quadratic function over an ellipsoid was formulated within a duality framework. Specifically, the applicability of Karush-Kuhn-Tucker conditions for global optimality for convex problems to the nonconvex case is established by showing the similarities between the nonconvex problem and the convex problem of the same type. Based on this fact, a dual program that contains the 'favorable features of linear programming duality' is described as a 'specialization of Lagrange duality.'

Restaurants, Duality theory (Mathematics)

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A low-rank bilinear programming approach for sub-optimal solution of the quadratic assignment problem

Article Abstract:

A new approximate algorithm based on low-rank bilinear programming for deriving sub-optimal solutions to quadratic assignment problems is introduced. The procedure, which requires the problem to be defined as a concave quadratic programming problem, approximates the negative semi-definite matrix Q using its eigenvalue structures to reduce the computational cost of solving the NP-hard problem.

Methods, Integer programming

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QUAD01: a data-structured implementation of Hansen's quadratic zero-one programming algorithm

Article Abstract:

Pierre Hansen's implicit-enumeration algorithm for solving constrained quadratic zero-one programming problems is implemented once anew in C language. The resulting QUAD01 program, which employs linked-lists, is faster than Hansen's original implementation in Fortran. This is borne out by experiments with problems characterized by 50-100 variables and 100-200 constraints.

Software, Linked lists, Algebra, Boolean, Boolean algebra

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