A Brief Conclusion

We conclude this brief book by emphasizing once again that it is just an introduction to the subject. We have considered the basic Lipschitz global optimization problem, i.e., global minimization of a multiextremal, non-differentiable Lipschitz function over a hyperinterval with a special emphasis on Peano curves, strategies for adaptive estimation of Lipschitz information, and acceleration of the search.

[1]  Yaroslav D. Sergeyev,et al.  A one-dimensional local tuning algorithm for solving GO problems with partially defined constraints , 2007, Optim. Lett..

[2]  Yaroslav D. Sergeyev,et al.  Global Search Based on Efficient Diagonal Partitions and a Set of Lipschitz Constants , 2006, SIAM J. Optim..

[3]  Clara Pizzuti,et al.  Acceleration Tools for Diagonal Information Global Optimization Algorithms , 2001, Comput. Optim. Appl..

[4]  Inmaculada García,et al.  Interval Branch and Bound Algorithm for Finding the First-Zero-Crossing-Point in One-Dimensional Functions , 2000, Reliab. Comput..

[5]  Y. Sergeyev,et al.  Sequential and parallel algorithms for global minimizing functions with Lipschitzian derivatives , 1999 .

[6]  Roman G. Strongin,et al.  Global Optimization: Fractal Approach and Non-redundant Parallelism , 2003, J. Glob. Optim..

[7]  Pasquale Daponte,et al.  Two methods for solving optimization problems arising in electronic measurements and electrical engineering , 1999, SIAM J. Optim..

[8]  Yaroslav D. Sergeyev Global one-dimensional optimization using smooth auxiliary functions , 1998, Math. Program..

[9]  Inmaculada García,et al.  Interval Algorithms for Finding the Minimal Root in a Set of Multiextremal One-Dimensional Nondifferentiable Functions , 2002, SIAM J. Sci. Comput..

[10]  Yaroslav D. Sergeyev,et al.  Parallel Information Algorithm with Local Tuning for Solving Multidimensional GO Problems , 1999, J. Glob. Optim..

[11]  Yaroslav D. Sergeyev,et al.  An algorithm for solving global optimization problems with nonlinear constraints , 1995, J. Glob. Optim..

[12]  Yaroslav D. Sergeyev,et al.  Acceleration of Univariate Global Optimization Algorithms Working with Lipschitz Functions and Lipschitz First Derivatives , 2013, SIAM J. Optim..

[13]  R. G. Strongin,et al.  A global minimization algorithm with parallel iterations , 1990 .

[14]  Yaroslav D. Sergeyev,et al.  Univariate Global Optimization with Multiextremal Non-Differentiable Constraints Without Penalty Functions , 2006, Comput. Optim. Appl..

[15]  Pasquale Daponte,et al.  An algorithm for finding the zero crossing of time signals with Lipschitzean derivatives , 1995 .

[16]  Pasquale Daponte,et al.  Fast detection of the first zero-crossing in a measurement signal set , 1996 .

[17]  Y. Sergeyev,et al.  Parallel Asynchronous Global Search and the Nested Optimization Scheme , 2001 .

[18]  Yaroslav D. Sergeyev,et al.  Lipschitz Global Optimization , 2011 .

[19]  Yaroslav D. Sergeyev Efficient Partition of N-Dimensional Intervals in the Framework of One-Point-Based Algorithms , 2011, ArXiv.

[20]  Ya. D. Sergeyev A Method Using Local Tuning for Minimizing Functions with Lipschitz Derivatives , 1997 .

[21]  Ya. D. Sergeyev Multidimensional global optimization using the first derivatives , 1999 .

[22]  Boglárka G.-Tóth,et al.  On an Efficient Use of Gradient Information for Accelerating Interval Global Optimization Algorithms , 2004, Numerical Algorithms.

[23]  Yaroslav D. Sergeyev,et al.  Lipschitz gradients for global optimization in a one-point-based partitioning scheme , 2012, J. Comput. Appl. Math..

[24]  José A. Martínez,et al.  New Interval Analysis Support Functions Using Gradient Information in a Global Minimization Algorithm , 2003, J. Glob. Optim..

[25]  Y. D. Sergeyev,et al.  Global Optimization with Non-Convex Constraints - Sequential and Parallel Algorithms (Nonconvex Optimization and its Applications Volume 45) (Nonconvex Optimization and Its Applications) , 2000 .

[26]  Roman G. Strongin,et al.  Global multidimensional optimization on parallel computer , 1992, Parallel Comput..

[27]  Yaroslav D. Sergeyev,et al.  A univariate global search working with a set of Lipschitz constants for the first derivative , 2009, Optim. Lett..

[28]  R. G. Strongin,et al.  Minimization of multiextremal functions under nonconvex constraints , 1986 .

[29]  V. A. Grishagin,et al.  Sequential and parallel algorithms for global optimization , 1994 .

[30]  Yaroslav D. Sergeyev,et al.  Index branch-and-bound algorithm for Lipschitz univariate global optimization with multiextremal constraints , 2001, J. Glob. Optim..

[31]  Y. Sergeyev Efficient Strategy for Adaptive Partition of N-Dimensional Intervals in the Framework of Diagonal Algorithms , 2000 .