Jiming Peng

Self-regular functions and new search directions for linear and semidefinite optimization

Abstract.In this paper, we introduce the notion of a self-regular function. Such a function is strongly convex and smooth coercive on its domain, the positive real axis. We show that any such function induces a so-called self-regular proximity function and a corresponding search direction for primal-dual path-following interior-point methods (IPMs) for solving linear optimization (LO) problems. It is proved that the new large-update IPMs enjoy a polynomial ?(n

Self-regularity : a new paradigm for primal-dual interior-point algorithms

\frac{q+1}{2q}

Scale invariant cosegmentation for image groups

log

Equivalence of variational inequality problems to unconstrained minimization

\frac{n}{\varepsilon}

Optimality Conditions for the Minimization of a Quadratic with Two Quadratic Constraints

) iteration bound, where q≥1 is the so-called barrier degree of the kernel function underlying the algorithm. The constant hidden in the ?-symbol depends on q and the growth degree p≥1 of the kernel function. When choosing the kernel function appropriately the new large-update IPMs have a polynomial ?(

Approximating K-means-type Clustering via Semidefinite Programming

\sqrt{n}

A non-interior continuation method for generalized linear complementarity problems

lognlog

A hybrid Newton method for solving the variational inequality problem via the D-gap function

\frac{n}{\varepsilon}

Optimal Nearly Analytic Discrete Approximation to the Scalar Wave Equation

) iteration bound, thus improving the currently best known bound for large-update methods by almost a factor

On Mehrotra-Type Predictor-Corrector Algorithms

\sqrt{n}