A Globally Convergent Augmented Lagrangian Pattern Search Algorithm for Optimization with General Constraints and Simple Bounds

By Robert Michael Lewis, Virginia Torczon. SIAM Journal on Optimization, 2002

320 citations recorded by the source corpus.

Subfields: Computational Mechanics, Computational Theory and Mathematics, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/11dfac974133548ce12a750b9fed4f9d14439752

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Citations in the corpus

Derivative-free optimization: a review of algorithms and comparison of software implementations (2012, background): “Recent works on the subject have led to significant progress by providing convergence proofs [5,9,31,34,76,80, 85,88,134], incorporating the use of surrogate models [22,24,127,131], and offering the first textbook that is exclusively devoted to this topic [35].”
Sourcebook of parallel computing (2003, unknown): “This approach led to the parallel direct-search (PDS) method [258, 937], and to the novel convergence theory for more general pattern search methods [55, 607, 608, 609, 610, 938, 939].”
Binary ORC (Organic Rankine Cycles) power plants for the exploitation of medium–low temperature geothermal sources – Part B: Techno-economic optimization (2014, unknown): “Therefore, a more ef ﬁ cient two-level optimization procedure has been implemented, tackling the outer level problem with the patter search method of Lewis and Torczon e 2002 [7] as represented in Fig.”
A hybrid GA–PS–SQP method to solve power system valve-point economic dispatch problems (2010, methodology): “In this study, the Pattern Search (PS) method handles constraints by using augmented Lagrangian to solve the nonlinear constrained economic dispatch problem [27–30].”
Mesh Adaptive Direct Search Algorithms for Constrained Optimization (2006, background): “The class of algorithms presented here differs significantly from previous GPS extensions [4, 22] to nonlinear constraints.”
A Pattern Search Filter Method for Nonlinear Programming without Derivatives (2001, background): “Assuming that the functions f and C are twice continuously differentiable and that the constraint Jacobian has full rank, Lewis and Torczon [ 24 ] propose and analyze a derivativefree procedure to handle general constraints.”
A surrogate-model-based method for constrained optimization (2000, unknown): “We do this without penalty constants or Lagrange multiplier estimates (as required in [21]) by formulating a step acceptance rule based on filter methods.”
p-Causality: Identifying Spatiotemporal Causal Pathways for Air Pollutants with Urban Big Data (2016, methodology): “In our case, we use pattern search algorithm [16] to optimize the updating order, thus reducing the search space of casual pathways of different pollutants.”
Application of pattern search method to power system valve-point economic load dispatch (2007, background): “For more explanation on how PS handles constraints refer to [18,20,21].”
Optimization by Direct Search: New Perspectives on Some Classical and Modern Methods (2003, methodology): “Another approach to using GSS methods for nonlinearly constrained problems is the augmented Lagrangian approach by Lewis and Torczon in [169].”