# zbMATH — the first resource for mathematics

##### Examples
 Geometry Search for the term Geometry in any field. Queries are case-independent. Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact. "Topological group" Phrases (multi-words) should be set in "straight quotation marks". au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted. Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff. "Quasi* map*" py: 1989 The resulting documents have publication year 1989. so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14. "Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic. dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles. py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses). la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

##### Operators
 a & b logic and a | b logic or !ab logic not abc* right wildcard "ab c" phrase (ab c) parentheses
##### Fields
 any anywhere an internal document identifier au author, editor ai internal author identifier ti title la language so source ab review, abstract py publication year rv reviewer cc MSC code ut uncontrolled term dt document type (j: journal article; b: book; a: book article)
A redistributed proximal bundle method for nonconvex optimization. (English) Zbl 1211.90183
Summary: Proximal bundle methods have been shown to be highly successful optimization methods for unconstrained convex problems with discontinuous first derivatives. This naturally leads to the question of whether proximal variants of bundle methods can be extended to a nonconvex setting. This work proposes an approach based on generating cutting-planes models, not of the objective function as most bundle methods do but of a local convexification of the objective function. The corresponding convexification parameter is calculated “on the fly” in such a way that the algorithm can inform the user as to what proximal parameters are sufficiently large that the objective function is likely to have well-defined proximal points. This novel approach, shown to be sound from both the objective function and subdifferential modelling perspectives, opens the way to create workable nonconvex algorithms based on nonconvex $\mathrm{𝒱𝒰}$ theory. Both theoretical convergence analysis and some encouraging preliminary numerical experience are provided.
##### MSC:
 90C26 Nonconvex programming, global optimization 49J52 Nonsmooth analysis (other weak concepts of optimality) 65K10 Optimization techniques (numerical methods) 49J53 Set-valued and variational analysis 49M05 Numerical methods in calculus of variations based on necessary conditions
PNEW