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Local Duality of Nonlinear Programs
It is shown that the second order sufficient (necessary) optimality condition for the dual of a nonlinear program is equivalent to the inverse of the Hessian of the Lagrangian being positive definiteExpand
  • 15
  • 3
On the Augmented Lagrangian
  • S. Han
  • Mathematics, Computer Science
  • Math. Oper. Res.
  • 1 February 1986
It is well known that, for a nonlinear program, any Karush--Kuhn--Tucker point that satisfies the second order sufficient condition is also a strict local minimum of the augmented Lagrangian with an underlying penalty parameter sufficiently large. Expand
  • 5
  • 2
Conjugate Cone Characterization of Positive Definite and Semidefinite Matrices.
Abstract Positive definite and semidefinite matrices are characterized in terms of positive definiteness and semidefiniteness on arbitrary closed convex cones in Rn. These results are obtained byExpand
  • 16
  • Open Access
An inertia theorem for symmetric matrices and its application to nonlinear programming
Abstract The relationship between the inertia of a symmetric real matrix and the inertia of its projection to a subspace is studied. The result is then used to characterize a Karush-Kuhn-Tucker pointExpand
  • 11
On the Hessian of Lagrangian and second order optimality conditions
For a constrained minimization problem, the restriction of a Hessian of Lagrangian to a tangent space of the feasible set can be used to detect whether a Karush–Kuhn–Tucker point is a local minimum,Expand
  • 6
Characterization of Positive Definite and Semidefinite Matrices via Quadratic Programming Duality.
Positive definite and semidefinite matrices induce well-known duality results in quadratic programming. The converse is established here. Thus if certain duality results hold for a pair of dualExpand
  • 5
  • Open Access
Identifying and Analyzing the Correlations and Inter-Causalities of the Root Causes of Construction Defects
Understanding defect causalities is indispensable to its prevention. This paper aims to identify the correlations and inter-causalities amongst the root causes of construction defects, so as toExpand
  • 1
  • Open Access
Relative eigenvalues of Hermitian matrices
  • S. Han
  • Mathematics
  • 1 September 1986
Abstract Motivated by the interest in a more thorough understanding of the relationship between the eigenvalues of a Hermitian matrix M and those of a matrix of the form A ∗ MA , we study theExpand
  • 6