A collection of test problems for constrained global optimization algorithms
A collection of test problems for constrained global optimization algorithms
Calmness and exact penalization
SIAM Journal on Control and Optimization
An exact penalization viewpoint of constrained optimization
SIAM Journal on Control and Optimization
Global minimization by reducing the duality gap
Mathematical Programming: Series A and B
Error bounds in mathematical programming
Mathematical Programming: Series A and B - Special issue: papers from ismp97, the 16th international symposium on mathematical programming, Lausanne EPFL
Lancelot: A FORTRAN Package for Large-Scale Nonlinear Optimization (Release A)
Lancelot: A FORTRAN Package for Large-Scale Nonlinear Optimization (Release A)
SNOPT: An SQP Algorithm for Large-Scale Constrained Optimization
SIAM Journal on Optimization
A Nonlinear Lagrangian Approach to Constrained Optimization Problems
SIAM Journal on Optimization
Decreasing Functions with Applications to Penalization
SIAM Journal on Optimization
Integrated coverage and connectivity configuration in wireless sensor networks
Proceedings of the 1st international conference on Embedded networked sensor systems
A Unified Augmented Lagrangian Approach to Duality and Exact Penalization
Mathematics of Operations Research
Co-Grid: an efficient coverage maintenance protocol for distributed sensor networks
Proceedings of the 3rd international symposium on Information processing in sensor networks
On greedy geographic routing algorithms in sensing-covered networks
Proceedings of the 5th ACM international symposium on Mobile ad hoc networking and computing
On Solving Nonconvex Optimization Problems by Reducing The Duality Gap
Journal of Global Optimization
Evolutionary algorithms, homomorphous mappings, and constrained parameter optimization
Evolutionary Computation
A geometric framework for nonconvex optimization duality using augmented lagrangian functions
Journal of Global Optimization
Near optimal rate selection for wireless control systems
ACM Transactions on Embedded Computing Systems (TECS)
Hi-index | 0.00 |
Duality is an important notion for nonlinear programming (NLP). It provides a theoretical foundation for many optimization algorithms. Duality can be used to directly solve NLPs as well as to derive lower bounds of the solution quality which have wide use in other high-level search techniques such as branch and bound. However, the conventional duality theory has the fundamental limit that it leads to duality gaps for nonconvex problems, including discrete and mixed-integer problems where the feasible sets are generally nonconvex.In this paper, we propose an extended duality theory for nonlinear optimization in order to overcome some limitations of previous dual methods. Based on a new dual function, the extended duality theory leads to zero duality gap for general nonconvex problems defined in discrete, continuous, and mixed spaces under mild conditions. Comparing to recent developments in nonlinear Lagrangian functions and exact penalty functions, the proposed theory always requires lesser penalty to achieve zero duality. This is very desirable as the lower function value leads to smoother search terrains and alleviates the ill conditioning of dual optimization.Based on the extended duality theory, we develop a general search framework for global optimization. Experimental results on engineering benchmarks and a sensor-network optimization application show that our algorithm achieves better performance than searches based on conventional duality and Lagrangian theory.