1,658 research outputs found
Second-order subdifferential calculus with applications to tilt stability in optimization
The paper concerns the second-order generalized differentiation theory of
variational analysis and new applications of this theory to some problems of
constrained optimization in finitedimensional spaces. The main attention is
paid to the so-called (full and partial) second-order subdifferentials of
extended-real-valued functions, which are dual-type constructions generated by
coderivatives of frst-order subdifferential mappings. We develop an extended
second-order subdifferential calculus and analyze the basic second-order
qualification condition ensuring the fulfillment of the principal secondorder
chain rule for strongly and fully amenable compositions. The calculus results
obtained in this way and computing the second-order subdifferentials for
piecewise linear-quadratic functions and their major specifications are applied
then to the study of tilt stability of local minimizers for important classes
of problems in constrained optimization that include, in particular, problems
of nonlinear programming and certain classes of extended nonlinear programs
described in composite terms
Some results related to constrained non-differentiable (non- smooth) pseudolinear minimization problems
This paper deals with the minimization of a class of non-differentiable (non- smooth) pseudolinear functions over a closed and convex set subject to linear inequality constraints. The properties of locally Lipschitz pseudolinear functions are used to establish several Lagrange multiplier characterizations of the solution set of the minimization problem. We derive certain conditions, under which an efficient solution becomes a properly efficient solution of a constrained non-differentiable minimization problem
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