Branch-delete-bound algorithm for globally solving quadratically constrained quadratic programs

Abstract

This paper presents a branch-delete-bound algorithm for effectively solving the global minimum of quadratically constrained quadratic programs problem, which may be nonconvex. By utilizing the characteristics of quadratic function, we construct a new linearizing method, so that the quadratically constrained quadratic programs problem can be converted into a linear relaxed programs problem. Moreover, the established linear relaxed programs problem is embedded within a branch-and-bound framework without introducing any new variables and constrained functions, which can be easily solved by any effective linear programs algorithms. By subsequently solving a series of linear relaxed programs problems, the proposed algorithm can converge the global minimum of the initial quadratically constrained quadratic programs problem. Compared with the known methods, numerical results demonstrate that the proposed method has higher computational efficiency.

[Retracted] Branch‐and‐Reduction Algorithm for Indefinite Quadratic Programming Problem

“…In the last decades, many algorithms have been proposed for globally solving the IQPP and its special forms. In these algorithms, most of them adopt the branch-andbound framework, for example, the branch-and-bound algorithm based on parametric linear relaxation [7], branch-and-bound outer approximation algorithm [8], branch-and-reduce algorithms based on linear relaxation [9][10][11][12][13][14][15][16][17][18], and branch-and-cut algorithm [19]. In these algorithms, to be specified, Gao et al [10,11] propose two novel branch-and-reduce approaches for the IQPP by employing a new rectangle partitioning method and some reducing tactics.…”

Modeling side slopes in vertical alignment resource road construction using convex optimization

“…It can be convex or nonconvex, and is generally NP‐hard making finding an optimal solution challenging; see Boyd and Vandenberghe (2004) for more details on QCQP. These problems arise in various fields: road construction, management science, stock exchange, production design, and so forth (Hou et al., 2017).…”

An Effective Global Optimization Algorithm for Quadratic Programs with Quadratic Constraints

“…In the last several decades, many algorithms have been developed for globally solving the (QPWQC) and its special cases, such as branch-and-bound method [12,13], approximation approach [14], robust approach [15], branch-reduce-bound algorithm [16][17][18][19], geometric programming approach [20][21][22][23], and others. Except for the above approaches, some global optimization algorithms [24][25][26][27][28][29][30][31][32][33][34][35][36][37][38] for linear multiplicative programming problems and generalized linear fractional programming problems can be used to solve the quadratic programs with quadratic constraints (QPWQC) considered in this paper.…”