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- Publications
- Influence

Local Duality of Nonlinear Programs

- O. Fujiwara, S. Han, O. Mangasarian
- Mathematics
- 1984

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 definite… Expand

On the Augmented Lagrangian

- S. Han
- Mathematics, Computer Science
- Math. Oper. Res.
- 1 February 1986

tl;dr

Conjugate Cone Characterization of Positive Definite and Semidefinite Matrices.

- S. Han, O. Mangasarian
- Mathematics
- 1984

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 by… Expand

An inertia theorem for symmetric matrices and its application to nonlinear programming

- S. Han, O. Fujiwara
- Mathematics
- 1 December 1985

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 point… Expand

On the Hessian of Lagrangian and second order optimality conditions

- S. Han
- Mathematics
- 1 May 1986

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

Characterization of Positive Definite and Semidefinite Matrices via Quadratic Programming Duality.

- S. Han, O. Mangasarian
- Mathematics
- 1 March 1984

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 dual… Expand

Identifying and Analyzing the Correlations and Inter-Causalities of the Root Causes of Construction Defects

- H. Aljassmi, J. Perera, S. Han
- Engineering
- 2013

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 to… Expand

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 the… Expand