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- Farid Alizadeh, Jean-Pierre A. Haeberly, Michael L. Overton
- SIAM Journal on Optimization
- 1998

Primal-dual interior-point path-following methods for semidefinite programming are considered. Several variants are discussed, based on Newtonâ€™s method applied to three equations: primal feasibility,â€¦ (More)

- Farid Alizadeh, Jean-Pierre A. Haeberly, Michael L. Overton
- Math. Program.
- 1997

Primal and dual nondegeneracy conditions are defined for semidefinite programming. Given the existence of primal and dual solutions, it is shown that primal nondegeneracy implies a unique dualâ€¦ (More)

- James V. Burke, Adrian S. Lewis, Michael L. Overton
- SIAM Journal on Optimization
- 2005

Let f be a continuous function on Rn, and suppose f is continuously differentiable on an open dense subset. Such functions arise in many applications, and very often minimizers are points at which fâ€¦ (More)

- Michael L. Overton, Robert S. Womersley
- Math. Program.
- 1993

This paper gives max characterizations for the sum of the largest eigen-values of a symmetric matrix. The elements which achieve the maximum provide a concise characterization of the generalizedâ€¦ (More)

- Michael L. Overton
- SIAM Journal on Optimization
- 1992

Optimization problems involving eigenvalues arise in many applications. Let x be a vector of real parameters and let A(x) be a continuously diierentiable symmetric matrix function of x. We consider aâ€¦ (More)

Multiobjective control design is known to be a difficult problem both in theory and practice. Our approach is to search for locally optimal solutions of a nonsmooth optimization problem that is builtâ€¦ (More)

- Knud D. Andersen, Edmund Christiansen, Andrew R. Conn, Michael L. Overton
- SIAM J. Scientific Computing
- 2000

The problem of minimizing a sum of Euclidean norms dates from the 17th century and may be the earliest example of duality in the mathematical programming literature. This nonsmooth optimizationâ€¦ (More)

- Gene H. Golub, Franklin T. Luk, Michael L. Overton
- ACM Trans. Math. Softw.
- 1981

We present a block Lanczos method for computing the greatest singular values and associated vectors of a large and sparse matrix, say A. Our algorithm does not transform A but accesses it through aâ€¦ (More)

- Adrian S. Lewis, Michael L. Overton
- Math. Program.
- 2013

We investigate the behavior of quasi-Newton algorithms applied to minimize a nonsmooth function f , not necessarily convex. We introduce an inexact line search that generates a sequence of nestedâ€¦ (More)

- Frank E. Curtis, Michael L. Overton
- SIAM Journal on Optimization
- 2012

We consider optimization problems with objective and constraint functions that may be nonconvex and nonsmooth. Problems of this type arise in important applications, many having solutions at pointsâ€¦ (More)