Cornelis Roos

A New and Efficient Large-Update Interior-Point Method for Linear Optimization

  • Jiming Peng
  • Cornelis Roos
  • Tamás Terlaky
    • Categories Linear, Cone and Semidefinite Programming Tags , , , ,

    Recently, the authors presented a new large-update primal-dual method for Linear Optimization, whose $O(n^\frac23\,\log\frac{n}{\e})$ iteration bound substantially improved the classical bound for such methods, which is $O\br{n\log\frac{n}{\e}}$. In this paper we present an improved analysis of the new method. The analysis uses some new mathematical tools developed before when we considered a whole family of … Read more

    On implementing a primal-dual interior-point method for conic quadratic optimization

  • Cornelis Roos
  • Erling D. Andersen
  • Tamás Terlaky
    • Categories Convex Optimization, Other Topics, Second-Order Cone Programming Tags , , , ,

    Conic quadratic optimization is the problem of minimizing a linear function subject to the intersection of an affine set and the product of quadratic cones. The problem is a convex optimization problem and has numerous applications in engineering, economics, and other areas of science. Indeed, linear and convex quadratic optimization is a special case. Conic … Read more

    A scaled Gauss-Newton Primal–Dual Search Direction for Semidefinite Optimization

  • Etienne de Klerk
  • Cornelis Roos
  • J Peng
  • Tamás Terlaky
    • Categories Linear, Cone and Semidefinite Programming, Semi-definite Programming Tags , ,

    Interior point methods for semidefinite optimization (SDO) have recently been studied intensively, due to their polynomial complexity and practical efficiency. Most of these methods are extensions of linear optimization (LO) algorithms. Unlike in the LO case, there are several different ways of constructing primal-dual search directions in SDO. The usual scheme is to apply linearization … Read more

    A New Class of Polynomial Primal-Dual Methods for Linear and Semidefinite Optimization

  • Cornelis Roos
  • J Peng
  • Tamás Terlaky
    • Categories Linear, Cone and Semidefinite Programming Tags , ,

    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 $O\br{n^{\frac{4}{4+\rho}}\log\frac{n}{\e}}$ iterations where $\rho\in [0,2]$ is a parameter used in the system defining the search direction. If $\rho=0$, … Read more