title: A deterministic annealing algorithm for approximating a solution of the linearly constrained nonconvex quadratic minimization problem.
abstract: A deterministic annealing algorithm is proposed for approximating a solution of the linearly constrained nonconvex quadratic minimization problem. The algorithm is derived from applications of a Hopfield-type barrier function in dealing with box constraints and Lagrange multipliers in handling linear equality constraints, and attempts to obtain a solution of good quality by generating a minimum point of a barrier problem for a sequence of descending values of the barrier parameter. For any given value of the barrier parameter, the algorithm searches for a minimum point of the barrier problem in a feasible descent direction, which has a desired property that the box constraints are always satisfied automatically if the step length is a number between zero and one. At each iteration, the feasible descent direction is found by updating Lagrange multipliers with a globally convergent iterative procedure. For any given value of the barrier parameter, the algorithm converges to a stationary point of the barrier problem. Preliminary numerical results show that the algorithm seems effective and efficient.
authors.affiliation: Department of Systems Engineering & Engineering Management, City University of Hong Kong, Kowloon, Hong Kong. mecdang@cityu.edu.hk
authors.forename: Chuangyin
authors.initials: C
authors.lastname: Dang
authors.forename: Jianqing
authors.initials: J
authors.lastname: Liang
authors.forename: Yang
authors.initials: Y
authors.lastname: Yang
mesh_terms: D000465:Algorithms; D055641:Mathematical Concepts; D016571:Neural Networks, Computer; D013696:Temperature