Minimization methods for non-differentiable functions
Minimization methods for non-differentiable functions
Power System Analysis and Design
Power System Analysis and Design
Discrete Time Control Problems Using MATLAB
Discrete Time Control Problems Using MATLAB
An Inverse Free Preconditioned Krylov Subspace Method for Symmetric Generalized Eigenvalue Problems
SIAM Journal on Scientific Computing
A New Matrix-Free Algorithm for the Large-Scale Trust-Region Subproblem
SIAM Journal on Optimization
Minimization of a Large-Scale Quadratic Function Subject to a Spherical Constraint
SIAM Journal on Optimization
Solving the Trust-Region Subproblem using the Lanczos Method
SIAM Journal on Optimization
Minimizing a Quadratic Over a Sphere
SIAM Journal on Optimization
Algorithm 845: EIGIFP: a MATLAB program for solving large symmetric generalized eigenvalue problems
ACM Transactions on Mathematical Software (TOMS)
Mathematical Programming: Series A and B
Introduction to Global Optimization (Nonconvex Optimization and Its Applications)
Introduction to Global Optimization (Nonconvex Optimization and Its Applications)
A multilevel algorithm for solving the trust-region subproblem
Optimization Methods & Software - THE JOINT EUROPT-OMS CONFERENCE ON OPTIMIZATION, 4-7 JULY, 2007, PRAGUE, CZECH REPUBLIC, PART II
An Ellipsoidal Branch and Bound Algorithm for Global Optimization
SIAM Journal on Optimization
A Subspace Minimization Method for the Trust-Region Step
SIAM Journal on Optimization
Infeasibility Detection and SQP Methods for Nonlinear Optimization
SIAM Journal on Optimization
A variable target value method for nondifferentiable optimization
Operations Research Letters
A two-stage non-linear program for optimal electrical grid power balance under uncertainty
Proceedings of the Winter Simulation Conference
Two-stage stochastic optimization for optimal power flow under renewable generation uncertainty
ACM Transactions on Modeling and Computer Simulation (TOMACS) - Special issue on simulation in complex service systems
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This paper investigates a Lagrangian dual problem for solving the optimal power flow problem in rectangular form that arises from power system analysis. If strong duality does not hold for the dual, we propose two classes of branch-and-bound algorithms that guarantee to solve the problem to optimality. The lower bound for the objective function is obtained by the Lagrangian duality, whereas the feasible set subdivision is based on the rectangular or ellipsoidal bisection. The numerical experiments are reported to demonstrate the effectiveness of the proposed algorithms. We note that no duality gap is observed for any of our test problems.