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We follow the popular approach for unconstrained minimization, i.e. we develop a local quadratic model at a current approximate minimizer in conjunction with a trust region. We then minimize this local model in order to nd the next approximate minimizer. Asymptot-ically, nding the local minimizer of the quadratic model is equivalent to applying Newton's… (More)

- Xuan Vinh Doan, Serge Kruk, Henry Wolkowicz
- Optimization Methods and Software
- 2012

Current successful methods for solving semidefinite programs, SDP, are based on primal-dual interior-point approaches. These usually involve a symmetrization step to allow for application of Newton’s method followed by block elimination to reduce the size of the Newton equation. Both these steps create ill-conditioning in the Newton equation and singularity… (More)

- Serge Kruk, Henry Wolkowicz
- SIAM Review
- 1999

This short note revisits an algorithm previously sketched by Mathis and Mathis, Siam Review 1995, and used to solve a nonlinear hospital fee optimization problem. An analysis of the problem structure reveals how the Simplex algorithm, viewed under the correct light, can be the driving force behind a successful algorithm for a nonlinear problem. 1 A… (More)

Presolving for linear programming is an essential ingredient in many commercial packages. This step eliminates redundant constraints and identically zero variables, and it identiies possible infeasibility and unboundedness. In semideenite programming, identically zero variables corresponds to lack of a constraint qualiication which can result in both… (More)

- Steffan Puwal, Bradley J. Roth, Serge Kruk
- Mathematical medicine and biology : a journal of…
- 2005

Electrical wave-fronts are responsible for contraction in heart tissue. Rotary wave-fronts break up into daughter waves and it is this break up that is believed to underlie ventricular fibrillation. Mathematical methods abound for simulation of fibrillation, and localizing the core of rotary wave-fronts (the phase singularities) is key to characterizing the… (More)

Primal-dualinterior-point methods have proven to be very successful for both linear programming (LP) and, more recently, for semideenite programming (SDP) problems. Many of the techniques that have been so successful for LP have been extended to SDP. In fact, interior point methods are currently the only successful techniques for SDP. We present a new… (More)

We prove the theoretical convergence of a short-step, approximate pathfollowing, interior-point primal-dual algorithm for semidefinite programs based on the Gauss-Newton direction obtained from minimizing the norm of the perturbed optimality conditions. This is the first proof of convergence for the Gauss-Newton direction in this context. It assumes strict… (More)

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