A Dual Decomposition Algorithm for Solving Mixed Integer-Continuous Quadratic Programming Problems

摘要

The report contains a presentation of an algorithm for solving the following mixed integer-continuous mathematical programming problem: min((g super T)y + (c superscript T)x + 1/2 (x superscript T)Dx: (Ax + By) > or = b, y is an element of S, x > or = O) where g, c, x, y, and b are column vectors of appropriate dimension; A, B, and D are matrices of appropriate dimension; and S is a closed bounded set whose elements have integer components. The quadratic form is assumed to be positive semi-definite. The algorithm is a generalization of one developed by J. F. Benders for solving the above problem for the special case where D = O. The primary motivation for developing this algorithm was a desire to construct a method for solving both an aircraft maintenance scheduling problem and the unit commitment - economic dispatch scheduling problem encountered in large scale power systems. (Author)