Johri's general dual, the Lagrangian dual, and the surrogate dual

Article Abstract:

The Lagrangian dual, the surrogate dual and Johri's general dual are three ways of duality formulation. The three utilize two devices to relax the primal problem into subproblems, namely functions which dominate the primal objective function and sets which include the primal feasible set. Such devices offer dual minimax-formulations in general nonlinear optimization. Analysis of the three duals also reveals that a specific dual's subproblems do not have to be either restrictions or relaxations of the primal problem.

Duality theory (Mathematics)

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Simple Lagrangian heuristic for the set covering problem

Article Abstract:

A Lagrangian heuristic of complexity O(m.f) for solving the NP-complete set covering problem (LHSCP) is introduced. The heuristic employs standard Lagrangian duality, greedy heuristic, redundant covers and subgradient optimization techniques. According to test runs of 65 benchmark problems on a Sun Sparc station of the SUN-Pascal-coded heuristic, it is efficient for SCPs with low density and large number of variables.

Case studies

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A Lagrangian relaxation approach to the edge-weighted clique problem

Article Abstract:

Research is presented describing the development of a Boolean quadric polytope mathematical programming solution aimed at relaxing the Lagrangain framework of operations management.

Methods, Algebra, Boolean, Boolean algebra

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