Global minimization algorithms for concave quadratic programming problems

Sign reversion approach to concave minimization problems

“…We say that the set Y = Y in (11) is right if ϕ * > −∞ and there exists x(y) ∈ D and denote by Y the family of these right sets. Proof In case (i), by duality, x * is a solution of problem (7). Then the assertion follows from Theorem 1 (ii).…”

“…[1][2][3][4] and the references therein. Besides, there exists an approach based on global optimality conditions and level set approximations; see [5,7,8] and the references therein.…”

Bilinear modeling solution approach for fixed charge network flow problems

“…A review of global optimization approaches for indefinite quadratic programming is given by Pardalos [25] whereas a general overview with applications is given by Floudas and Visweswaran [9]. Specialized algorithms for concave, linear constrained quadratic programming have been developed by Konno [19], Bomze and Danninger [2] as well as Chinchuluun et al [5]. A parallel algorithm was introduced by Phillips and Rosen [27].…”

Development of a Procedure for Finding Active Points of Linear Constraints

“…In most optimization problems, initialization points are necessary and required in the resolution algorithms for performing numerical implementations [6][7][8]11,12]. However, the choice of the initialization points is not general, and the values of these points depend strongly on the adopted technique.…”

“…The various existing techniques for solving a given problem and the efficient algorithmic implementations open up many perspectives and diverse applications in different areas [6][7][8].…”