Results 31 to 40 of about 451 (54)
Robust Necessary Optimality Conditions for Nondifferentiable Complex Fractional Programming with Uncertain Data. [PDF]
J Optim Theory Appl, 2021 Chen J +4 more
europepmc +1 more source
Tilt stability, uniform quadratic growth, and strong metric regularity of the subdifferential [PDF]
arXiv, 2012 We prove that uniform second order growth, tilt stability, and strong metric regularity of the limiting subdifferential --- three notions that have appeared in entirely different settings --- are all essentially equivalent for any lower-semicontinuous, extended-real-valued function.
arxiv
Optimality, identifiability, and sensitivity [PDF]
arXiv, 2012 Around a solution of an optimization problem, an "identifiable" subset of the feasible region is one containing all nearby solutions after small perturbations to the problem. A quest for only the most essential ingredients of sensitivity analysis leads us to consider identifiable sets that are "minimal".
arxiv
Gauge Brezis-Browder Principles and Dependent Choice [PDF]
arXiv, 2013 The gauge Brezis-Browder Principle in Turinici [Bull. Acad. Pol. Sci. (Math.), 30 (1982), 161-166] is obtainable from the Principle of Dependent Choices (DC) and implies Ekeland's Variational Principle (EVP); hence, it is equivalent with both (DC) and (EVP).
arxiv
Second-order growth, tilt stability, and metric regularity of the subdifferential [PDF]
arXiv, 2013 This paper sheds new light on several interrelated topics of second-order variational analysis, both in finite and infinite-dimensional settings. We establish new relationships between second-order growth conditions on functions, the basic properties of metric regularity and subregularity of the limiting subdifferential, tilt-stability of local ...
arxiv
About uniform regularity of collections of sets [PDF]
Serdica Math. J. 39 (2013), 287-312, 2013 We further investigate the uniform regularity property of collections of sets via primal and dual characterizing constants. These constants play an important role in determining convergence rates of projection algorithms for solving feasibility problems.
arxiv
Brøndsted-Rockafellar property of subdifferentials of prox-bounded functions [PDF]
arXiv, 2013 We provide a new proof that the subdifferential of a proper lower semicontinuous convex function on a Banach space is maximal monotone by adapting the pattern commonly used in the Hilbert setting. We then extend the arguments to show more precisely that subdifferentials of proper lower semicontinuous prox-bounded functions possess the Br{\o}ndsted ...
arxiv
Quadratic growth and critical point stability of semi-algebraic functions [PDF]
arXiv, 2013 We show that quadratic growth of a semi-algebraic function is equivalent to strong metric subregularity of the subdifferential --- a kind of stability of generalized critical points. In contrast, this equivalence can easily fail outside of the semi-algebraic setting.
arxiv
Finitely convergent algorithm for nonconvex inequality problems [PDF]
arXiv, 2014 We extend Fukushima's result on the finite convergence of an algorithm for the global convex feasibility problem to the local nonconvex case.
arxiv
Sweeping by a tame process [PDF]
arXiv, 2014 We show that any semi-algebraic sweeping process admits piecewise absolutely continuous solutions, and any such bounded trajectory must have finite length. Analogous results hold more generally for sweeping processes definable in o-minimal structures. This extends previous work on (sub)gradient dynamical systems beyond monotone sweeping sets.
arxiv