Full Stability of Locally Optimal Solutions in Second-Order Cone Programs

  title={Full Stability of Locally Optimal Solutions in Second-Order Cone Programs},
  author={Boris S. Mordukhovich and Jir{\'i} V. Outrata and M. Ebrahim Sarabi},
  journal={SIAM J. Optim.},
The paper presents complete characterizations of Lipschitzian full stability of locally optimal solutions to second-order cone programs (SOCPs) expressed entirely in terms of their initial data. These characterizations are obtained via appropriate versions of the quadratic growth and strong second-order sufficient conditions under the corresponding constraint qualifications. We also establish close relationships between full stability of local minimizers for SOCPs and strong regularity of the… 

Second-Order Analysis of Piecewise Linear Functions with Applications to Optimization and Stability

Second-order variational analysis of a rather broad class of extended-real-valued piecewise liner functions and their applications to various issues of optimization and stability establishes relationships between nondegeneracy and second-order qualification for fully amenable compositions involving piecewise linear functions.

Full Stability in Finite-Dimensional Optimization

Developing a new technique of variational analysis and generalized differentiation, second-order characterizations of full stability are derived, in both Lipschitzian and Holderian settings, and established their relationships with the conventional notions of strong regularity and strong stability for a large class of problems of constrained optimization with twice continuously differentiable data.

Characterizations of Tilt-Stable Minimizers in Second-Order Cone Programming

This paper develops an approach of second-order variational analysis, which allows to establish complete neighborhood and pointbased characterizations of tilt stability for problems ofsecond-order cone programming generated by the nonpolyhedral second- order/Lorentz/ice-cream cone.

Local Monotonicity and Full Stability for Parametric Variational Systems

New notions of Lipschitzian and Holderian full stability of solutions to general parametric variational systems defined via partial subdifferential of prox-regular functions acting in finite-dimensional and Hilbert spaces are introduced.

Augmented Lagrangian method for second-order cone programs under second-order sufficiency

This paper addresses problems of second-order cone programming important in optimization theory and applications by formulate the corresponding version ofsecond-order sufficiency and use it to establish the uniform second- order growth condition for the augmented Lagrangian.

Second-Order Optimality Conditions for Constrained Optimization Problems with $$C^1$$ Data Via Regular and Limiting Subdifferentials

We present the second-order point-based (necessary and sufficient) optimality conditions for nonlinear programming with continuously differentiable data, via the regular and limiting (Mordukhovich)

Local strong maximal monotonicity and full stability for parametric variational systems

The paper introduces and characterizes new notions of Lipschitzian and H\"olderian full stability of solutions to general parametric variational systems described via partial subdifferential and

Complete Characterizations of Tilt Stability in Nonlinear Programming under Weakest Qualification Conditions

This paper derives here complete pointbased second-order characterizations of tilt-stable minimizers entirely in terms of the initial program data under the new qualification conditions, which are the weakest ones for the study of tilt stability.

Stability Analysis for Composite Optimization Problems and Parametric Variational Systems

This paper focuses here on establishing relationships between full stability of local minimizers in composite optimization and Robinson’s strong regularity of associated (linearized and nonlinearized) KKT systems.



Characterizations of Full Stability in Constrained Optimization

Based on second-order generalized differential tools of variational anal- ysis, necessary and sufficient conditions are obtained for fully stable local minimizers in general classes of constrained optimization problems, including problems of composite optimization, mathemati- cal programs with polyhedral constraints, as well as problems of extended and classical nonlinear programming with twice continuously differentiable data.

Second-Order Variational Analysis in Conic Programming with Applications to Optimality and Stability

A second-order generalized differential approach of variational analysis to calculate appropriate derivatives and coderivatives of the corresponding solution maps of conic programming modeled via parameter-dependent generalized equations is developed.

On the Aubin Property of Critical Points to Perturbed Second-Order Cone Programs

The Aubin property of a canonically perturbed KKT system related to the second-order cone programming problem in terms of a strong second- order optimality condition that is equivalent with the Robinson strong regularity.

Stability of Locally Optimal Solutions

Property of prox-regularity of the essential objective function and positive definiteness of its coderivative Hessian are the keys to the Lipschitzian stability of local solutions to finite-dimensional parameterized optimization problems in a very general setting.

Second-order characterizations of tilt stability with applications to nonlinear programming

A new approach to tilt stability is developed, which allows for not only qualitative but also quantitative characterizations of tilt-stable minimizers with calculating the corresponding moduli under new second-order qualification and optimality conditions.

Partial Second-Order Subdifferentials in Variational Analysis and Optimization

This article presents a systematic study of partial second-order subdifferentials for extended-real-valued functions, which have already been applied to important issues of variational analysis and

Second-Order Subdifferential Calculus with Applications to Tilt Stability in Optimization

The main focus is the so-called (full and partial) second- order subdifferentials of extended-real-valued functions, which are dual-type constructions generated by coderivatives of first-order subdifferential mappings.

Perturbation analysis of second-order cone programming problems

A characterization of strong regularity in terms of second order optimality conditions for nonpolyhedral conic problem is given, the first time such a characterization is given for a nonPolyhedral Conic problem.

Second-order growth, tilt stability, and metric regularity of the subdifferential

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