Papers by JEAN-PIERRE HAEBERLY
SDPPACK User''s Guide -- Version 0.9 Beta for Matlab 5.0
This report describes SDPpack Version 0.9 Beta for Matlab 5.0. This version extends the previous ... more This report describes SDPpack Version 0.9 Beta for Matlab 5.0. This version extends the previous release for semidefinite programming (SDP) to mixed semidefinite--quadratic--linear programs (SQLP), i.e.\ linear optimization problems over a product of semidefinite cones, quadratic cones and the nonnegative orthant. Together, these cones make up all possible homogeneous self-dual cones over the reals. The main routine implements a primal--dual Mehrotra predictor--corrector scheme based on the XZ+ZX search direction for SDP. More specialized routines are also available, one to solve SDP''s with diagonal constraints only, and one to compute the Lov\''asz $\theta$ function of a graph, both using the XZ search direction. Routines are also provided to determine whether an SQLP is primal or dual degenerate at its solution and whether strict complementarity holds there. Primal nondegeneracy is associated with dual uniqueness and dual nondegeneracy with primal uniqueness, thou...
Sdppack User's Guide
. This report describes SDPpack, a package of Matlab files designedto solve semidefinite programs... more . This report describes SDPpack, a package of Matlab files designedto solve semidefinite programs (SDP). SDP is a generalization of linear programmingto the space of block diagonal, symmetric, positive semidefinitematrices. The main routine implements a primal--dual Mehrotra predictor--corrector scheme based on the XZ+ZX search direction. We also provide certainspecialized routines, one to solve SDP's with only diagonal constraints,and one to
We investigate numerically a 1956 conjecture of Payne, Polya, and Weinberger. The conjecture asse... more We investigate numerically a 1956 conjecture of Payne, Polya, and Weinberger. The conjecture asserts that the ratio of the first two eigenvalues of the Laplacian on a bounded domainOmega of the plane with Dirichlet boundary conditions reaches its minimum value precisely whenOmega is a disk. A crucial feature of this problem is the loss of smoothness of the objective function at the solution. The following results form the core of our numerical treatment. First, we construct finite dimensional families of deformations of a disk equipped with a uniform triangulation. This permits the formulation of a discrete model of the problem via finite element techniques. Second, we build on the work of M. Overton to derive optimality conditions in terms of Clarke's generalized gradients for nonsmooth functions. These ideas are then combined into an algorithm and implemented in Fortran. Contents 1 Introduction 2 2 Preliminaries 4 3 Max characterization of P k i=1 i for symmetric matrices 8 4 ...
For G=S 1 there is no G-Chern character
Mixed semidefinite-quadratic-linear programs
Google, Inc. (search), Subscribe (Full Service), Register (Limited Service, Free), Login. Search:... more Google, Inc. (search), Subscribe (Full Service), Register (Limited Service, Free), Login. Search: The ACM Digital Library The Guide. ...
Proceedings of 1994 American Control Conference - ACC '94, 1994
We consider the following quasiconvex optimization problem: minimize the largest eigenvalue of a ... more We consider the following quasiconvex optimization problem: minimize the largest eigenvalue of a symmetric de nite matrix pencil depending on parameters. A new form of optimality conditions is given, emphasizing a complementarity condition on primal and dual matrices. Newton's method is then applied to these conditions to give a new quadratically convergent interior-point method which works well in practice. The algorithm is closely related to primaldual interior-point methods for semide nite programming.
2. Mixed Semidefinite—Quadratic—Linear Programs
Advances in Linear Matrix Inequality Methods in Control, 2000
Remarks on a Numerical Study of Convexity, Quasiconvexity, and Rank One Convexity
Variational Methods for Discontinuous Structures, 1995
ABSTRACT In the calculus of variations, the notions of convexity, quasiconvexity, and rank one co... more ABSTRACT In the calculus of variations, the notions of convexity, quasiconvexity, and rank one convexity play an important role. In this paper we will discuss some numerical results concerning these notions.
Mixed Semidefinite-Quadratic-Linear Programs
We consider mixed semidenite{quadratic{linear programs. These arelinear optimization problems wit... more We consider mixed semidenite{quadratic{linear programs. These arelinear optimization problems with three kinds of cone constraints, namely:the semidenite cone, the quadratic cone and the nonnegative orthant. Weoutline a primal{dual path following method to solve these problems andhighlight the main features of SDPpack, a Matlab package which solvessuch programs. We give some examples where such mixed programs arise,and provide numerical results on
SDPPACK User''s Guide--Version 0.9 Beta for Matlab 5.0
This report describes SDPpack Version 0.9 Beta for Matlab 5.0. This version extends the previous ... more This report describes SDPpack Version 0.9 Beta for Matlab 5.0. This version extends the previous release for semidefinite programming (SDP) to mixed semidefinite--quadratic--linear programs (SQLP), ie\ linear optimization problems over a product of ...
A generalization of the segal conjecture
Topology, 1988
A generalization of the atiyah-segal completion theorem
Topology, 1988
A Hybrid Algorithm for Optimizing Eigenvalues of Symmetric Definite Pencils
SIAM Journal on Matrix Analysis and Applications, 1994
Abstract. We present an algorithm for the optimization of the maximum eigenvalue of a symmetric d... more Abstract. We present an algorithm for the optimization of the maximum eigenvalue of a symmetric de nite pencil depending a nely on a vector of parameters. The algorithm uses a hybrid approach, combining a scheme based on the method of centers, developed by Boyd and ...
Proceedings of the Royal Society of Edinburgh: Section A Mathematics, 1996
We provide an explicit example of a function that is homogeneous of degree one, rank-one convex, ... more We provide an explicit example of a function that is homogeneous of degree one, rank-one convex, but not convex.
Extending Mehrotra and Gondzio higher order methods to mixed semidefinite-quadratic-linear programming
Optimization Methods and Software, 1999
. We discuss extensions of Mehrotra's higher order corrections scheme and Gondzio's mul... more . We discuss extensions of Mehrotra's higher order corrections scheme and Gondzio's multiple centrality corrections scheme to mixed semidenitequadratic -linear programming (SQLP). These extensions have been included in a solver for SQLP written in C and based on LAPACK. ...
Optimization over symmetric cones
Page 1. Optimization Over Symmetric Cones by Madhu V. Nayakkankuppam ... Last revised: April 3, 2... more Page 1. Optimization Over Symmetric Cones by Madhu V. Nayakkankuppam ... Last revised: April 3, 2000. Page 2. c Madhu V. Nayakkankuppam All Rights Reserved 2000 Page 3. For Amma, Appa, Doonda, and in fond memory of Patti, who all took so little and gave so much iii ...
Sdppack User's Guide-VERSION BETA FOR MATLAB 5.0
ABSTRACT . This report describes SDPpack Version 0.9 Beta for Matlab 5.0. This version extends th... more ABSTRACT . This report describes SDPpack Version 0.9 Beta for Matlab 5.0. This version extends the previous release for semidefinite programming (SDP) to mixed semidefinite--quadratic--linear programs (SQLP), i.e. linear optimization problems over a product of semidefinite cones, quadratic cones and the nonnegative orthant. Together, these cones make up all possible homogeneous self-dual cones over the reals. The main routine implements a primal--dual Mehrotra predictor--corrector scheme based on the XZ+ZX search direction for SDP. More specialized routines are also available, one to solve SDP's with diagonal constraints only, and one to compute the Lov'asz ` function of a graph, both using the XZ search direction. Routines are also provided to determine whether an SQLP is primal or dual degenerate at its solution and whether strict complementarity holds there. Primal nondegeneracy is associated with dual uniqueness and dual nondegeneracy with primal uniqueness, though these condit...
SIAM Journal on Optimization, 1998
Primal-dual interior-point path-following methods for semide nite programming (SDP) are considere... more Primal-dual interior-point path-following methods for semide nite programming (SDP) are considered. Several variants are discussed, based on Newton's method applied to three equations: primal feasibil-ity, dual feasibility, and some form of centering condition. ...
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Papers by JEAN-PIERRE HAEBERLY