Tamás Terlaky

A Monotonic Build-Up Simplex Algorithm for Linear Programming

\sqrt n

Central Path Curvature and Iteration-Complexity for Redundant Klee—Minty Cubes

∣logε∣) orO((1+M2)n∣logε∣), depending on the updating scheme for the lower bound.

How good are interior point methods? Klee–Minty cubes tighten iteration-complexity bounds

Recently the authors introduced the notions of self-regular functions and self-regular proximity functions and used them in the design and analysis of interior-point methods (IPMs) for linear and semidefinite optimization (LO and SDO). In this paper, we consider an extension of these concepts to second-order conic optimization (SOCO). This nontrivial extension requires the development of various new tools. Versatile properties of general analytical functions associated with the second-order cone are exploited. Based on the so-called self-regular proximity functions, new primal-dual Newton methods for solving SOCO problems are proposed. It will be shown that these new large-update IPMs for SOCO enjoy polynomial

A potential reduction approach to the frequency assignment problem

{\cal{O}}({\max\{p,q\} N^{(q+1)/{2q}}\log \frac{N}{\e}})

Interior-Point Methodology for Linear Programming: Duality, Sensitivity Analysis and Computational Aspects

iteration bounds analogous to those of their LO and SDO cousins, where N is the number of constraining cones and p,q are constants, the so-called growth degree and barrier degree of the corresponding proximity. Our analysis allows us to choose not only a constant q but also a q as large as logN. In this case, our new algorithm has the best known

Sensitivity Analysis in Linear Semi-Infinite Programming via Partitions

{\cal{O}}({N^{1/2}\log{N}\log\frac{N}{\e}})

On routing in VLSI design and communication networks

iteration bound for large-update IPMs.

The role of pivoting in proving some fundamental theorems of linear algebra

In this paper, we propose a method for linear programming with the property that, starting from an initial non-central point, it generates iterates that simultaneously get closer to optimality and closer to centrality. The iterates follow paths that in the limit are tangential to the central path. Together with the convergence analysis, we provide a general framework which enables us to analyze various primal-dual algorithms in the literature in a short and uniform way.

A polynomial path-following interior point algorithm for general linear complementarity problems

Abstract We propose a new class of primal–dual methods for linear optimization (LO). By using some new analysis tools, we prove that the large-update method for LO based on the new search direction has a polynomial complexity of O(n4/(4+ρ)log(n/e)) iterations, where ρ∈[0,2] is a parameter used in the system defining the search direction. If ρ=0, our results reproduce the well-known complexity of the standard primal–dual Newton method for LO. At each iteration, our algorithm needs only to solve a linear equation system. An extension of the algorithms to semidefinite optimization is also presented.