ACM Transactions on Mathematical Software (TOMS)
Simulated annealing and Boltzmann machines: a stochastic approach to combinatorial optimization and neural computing
CUTE: constrained and unconstrained testing environment
ACM Transactions on Mathematical Software (TOMS)
Cycle Decompositions and Simulated Annealing
SIAM Journal on Control and Optimization
Asymptotic analysis for penalty and barrier methods in convex and linear programming
Mathematics of Operations Research
SNOPT: An SQP Algorithm for Large-Scale Constrained Optimization
SIAM Journal on Optimization
Simulated Annealing with Asymptotic Convergence for Nonlinear Constrained Global Optimization
CP '99 Proceedings of the 5th International Conference on Principles and Practice of Constraint Programming
The Theory of Discrete Lagrange Multipliers for Nonlinear Discrete Optimization
CP '99 Proceedings of the 5th International Conference on Principles and Practice of Constraint Programming
Global optimization for constrained nonlinear programming (asymptotic convergence)
Global optimization for constrained nonlinear programming (asymptotic convergence)
The theory and applications of discrete constrained optimization using lagrange multipliers
The theory and applications of discrete constrained optimization using lagrange multipliers
Constraint partitioning in penalty formulations for solving temporal planning problems
Artificial Intelligence
Solving nonlinear constrained optimization problems through constraint partitioning
Solving nonlinear constrained optimization problems through constraint partitioning
Effective method for constrained minimum - reverse bridge theorem
Computers & Mathematics with Applications
Computers and Operations Research
A dynamic convexized method for nonconvex mixed integer nonlinear programming
Computers and Operations Research
A particle swarm-BFGS algorithm for nonlinear programming problems
Computers and Operations Research
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In this paper, we present constrained simulated annealing (CSA), an algorithm that extends conventional simulated annealing to look for constrained local minima of nonlinear constrained optimization problems. The algorithm is based on the theory of extended saddle points (ESPs) that shows the one-to-one correspondence between a constrained local minimum and an ESP of the corresponding penalty function. CSA finds ESPs by systematically controlling probabilistic descents in the problem-variable subspace of the penalty function and probabilistic ascents in the penalty subspace. Based on the decomposition of the necessary and sufficient ESP condition into multiple necessary conditions, we present constraint-partitioned simulated annealing (CPSA) that exploits the locality of constraints in nonlinear optimization problems. CPSA leads to much lower complexity as compared to that of CSA by partitioning the constraints of a problem into significantly simpler subproblems, solving each independently, and resolving those violated global constraints across the subproblems. We prove that both CSA and CPSA asymptotically converge to a constrained global minimum with probability one in discrete optimization problems. The result extends conventional simulated annealing (SA), which guarantees asymptotic convergence in discrete unconstrained optimization, to that in discrete constrained optimization. Moreover, it establishes the condition under which optimal solutions can be found in constraint-partitioned nonlinear optimization problems. Finally, we evaluate CSA and CPSA by applying them to solve some continuous constrained optimization benchmarks and compare their performance to that of other penalty methods.