TITLE

Approximate Augmented Lagrangian Functions and Nonlinear Semidefinite Programs

AUTHOR(S)
Huang, X. X.; Teo, K. L.; Yang, X. Q.
PUB. DATE
September 2006
SOURCE
Acta Mathematica Sinica;Sep2006, Vol. 22 Issue 5, p1283
SOURCE TYPE
Academic Journal
DOC. TYPE
Article
ABSTRACT
In this paper, an approximate augmented Lagrangian function for nonlinear semidefinite programs is introduced. Some basic properties of the approximate augmented Lagrange function such as monotonicity and convexity are discussed. Necessary and sufficient conditions for approximate strong duality results are derived. Conditions for an approximate exact penalty representation in the framework of augmented Lagrangian are given. Under certain conditions, it is shown that any limit point of a sequence of stationary points of approximate augmented Lagrangian problems is a KKT point of the original semidefinite program and that a sequence of optimal solutions to augmented Lagrangian problems converges to a solution of the original semidefinite program.
ACCESSION #
21745883

 

Related Articles

  • Duality Theorems of Multiobjective Generalized Disjunctive Fuzzy Nonlinear Fractional Programming. Ammar, E. E. // International Journal of Mathematical Combinatorics;Jun2011, Vol. 2, p1 

    This paper is concerned with the study of duality conditions to convex-concave generalized multiobjective fuzzy nonlinear fractional disjunctive programming problems for which the decision set is the union of a family of convex sets. The Lagrangian function for such problems is defined and the...

  • Optimality conditions and duality for nondifferentiable multiobjective fractional programming with generalized convexity. Chinchuluun, Altannar; Yuan, Dehui; Pardalos, Panos M. // Annals of Operations Research;Oct2007, Vol. 154 Issue 1, p133 

    In this paper, we consider nondifferentiable multiobjective fractional programming problems. A concept of generalized convexity, which is called ( C, a, ?, d)-convexity, is first discussed. Based on this generalized convexity, we obtain efficiency conditions for multiobjective fractional...

  • Mixed type second-order symmetric duality under F-convexity. Gulati, Tilak Raj; Verma, Khushboo // International Journal of Optimization & Control: Theories & Appl;Jan2013, Vol. 3 Issue 1, p1 

    We introduce a pair of second order mixed symmetric dual problems. Weak, strong and converse duality theorems for this pair are established under F-convexity assumptions.

  • Higher-Order Duality for Minimax Fractional Type Programming Involving Symmetric Matrices. Caiyun Jin; Cao-Zong Cheng // Applied Mathematics;Nov2011, Vol. 2 Issue 11, p1387 

    Convexity and generalized convexity play important roles in optimization theory. With the development of programming problem, there has been a growing interest in the higher-order dual problem and a lot of related generalized convexities are given. In this paper, we give the convexity of (F,...

  • Second-Order Duality for Nondifferentiable Minimax Fractional Programming Involving (F, p)-Convexity. Gupta, S. K.; Dangar, Debasis // International MultiConference of Engineers & Computer Scientists;2012, Vol. 2, p1 

    We focus our study to formulate two different types of second-order dual models for a nondifferentiable minimax fractional programming problem and derive duality theorems under (F, p)-convexity. Several results including many recent works are obtained as special cases.

  • Conic version of Loewner-John ellipsoid theorem. Seeger, Alberto; Torki, Mounir // Mathematical Programming;Jan2016, Vol. 155 Issue 1/2, p403 

    We extend John's inscribed ellipsoid theorem, as well as Loewner's circumscribed ellipsoid theorem, from convex bodies to proper cones. To be more precise, we prove that a proper cone $$K$$ in $$\mathbb {R}^n$$ contains a unique ellipsoidal cone $$Q^\mathrm{in}(K)$$ of maximal canonical volume...

  • SECOND ORDER CONVERSE DUALITY FOR NONLINEAR PROGRAMMING. Ahmadi, I.; Agarwal, Ravi P. // Journal of Nonlinear Sciences & Applications (JNSA);2010, Vol. 3 Issue 4, p234 

    Chandra and Abha [European J. Oper. Res. 122 (2000), 161-165] considered a nonlinear programming problem over cone constraints and presented the correct forms of its four types of duals formulated by Nanda and Das [European J. Oper. Res. 88 (1996) 572-577]. Yang et al. [Indian J. Pure Appl....

  • Signals in nonlinear electrodynamics invariant under duality rotations. Salazar Ibarguen, Humberto; García, A.; Plebanski, J. // Journal of Mathematical Physics;Nov89, Vol. 30 Issue 11, p2689 

    The signal propagation in nonlinear electrodynamics when an arbitrary Einstein–Born–Infeld theory is invariant under duality rotations is discussed. The quasimetric defining the characteristic surfaces that depend on the structural function is obtained. The propagation of nonlinear...

  • A duality approach to problems of combined stopping and deciding under constraints. Balzer, Thomas; Janßen, Klaus // Mathematical Methods of Operations Research;2002, Vol. 55 Issue 3, p431 

    A problem of combined stopping and deciding under constraints for continuous-time processes on a Brownian filtration is considered. Under certain regularity conditions on the admissible class of stopping times and decision processes it is possible to show that there is no duality gap between the...

Share

Read the Article

Courtesy of THE LIBRARY OF VIRGINIA

Sorry, but this item is not currently available from your library.

Try another library?
Sign out of this library

Other Topics