We consider the problem of minimizing an indefinite quadratic objective function subject to twosided indelinite quadratic constraints. Under a suitable simultaneous diagonalization assumption {which trivially holds for trust region type problems), we prove that the original problem is equivalent to a convex minimization problem with simple linear constraints. We then consider a special problem ...

We show that SDP (semidefinite programming) and SOCP (second order cone programming) relaxations provide exact optimal solutions for a class of nonconvex quadratic optimization problems. It is a generalization of the results by S. Zhang for a subclass of quadratic maximization problems that have nonnegative off-diagonal coefficient matrices of objective quadratic functions and diagonal coeffici...

The Economic Load Dispatch (ELD) problems in power generation systems are to reduce the fuel cost by reducing the total cost for the generation of electric power. This paper presents an efficient Modified Firefly Algorithm (MFA), for solving ELD Problem. The main objective of the problems is to minimize the total fuel cost of the generating units having quadratic cost functions subjected to lim...

this paper presents a parameterization method to optimal trajectory planning and dynamic obstacle avoidance for omni-directional robots. the aim of trajectory planning is minimizing a quadratic cost function while a maximum limitation on velocity and acceleration of robot is considered. first, we parameterize the trajectory using polynomial functions with unknown coefficients which transforms t...

We introduce the quadratic balanced optimization problem (QBOP) which can be used to model equitable distribution of resources with pairwise interaction. QBOP is strongly NP-hard even if the family of feasible solutions has a very simple structure. Several general purpose exact and heuristic algorithms are presented. Results of extensive computational experiments are reported using randomly gen...

We consider a proximal operator given by a quadratic function subject to bound constraints and give an optimization algorithm using the alternating direction method of multipliers (ADMM). The algorithm is particularly efficient to solve a collection of proximal operators that share the same quadratic form, or if the quadratic program is the relaxation of a binary quadratic problem.