Iterative regularization in intensity-modulated radiation therapy optimization
Medical Physics — January 2006 — Volume 33, Issue 1, pp. 225-234. CitationMedical Physics — January 2006 — Volume 33, Issue 1, pp. 225-234.
Projective Pre-Conditioners for Improving the Behavior of a Homogeneous Conic Linear System
We present a general theory for transforming a homogeneous conic system F: Ax = 0, x \in C, x \ne 0, to an equivalent system via projective transformation induced by the choice of a point in a related dual set. Such a projective transformation serves to pre-condition the conic system into a system that has … Read more
An Extension of the Conjugate Directions Method With Orthogonalization to Large-Scale Problems With Bound Constraints
In our reports on GAMM-04 and ECCOMAS-04 there has been presented a new conjugate directions method for large scale unconstrained minimization problems. High efficiency of this method is ensured by employing an orthogonalization procedure: when constructing the next conjugate vector the component of the gradient is used that is orthogonal to the subspace of preceding … Read more
An Explicit Semidefinite Characterization of Satisfiability for Tseitin Instances
This paper is concerned with the application of semidefinite programming to the satisfiability problem, and in particular with using semidefinite liftings to efficiently obtain proofs of unsatisfiability. We focus on the Tseitin satisfiability instances which are known to be hard for many proof systems. We present an explicit semidefinite programming problem with dimension linear in … Read more
Interior-Point l_2 Penalty Methods for Nonlinear Programming with Strong Global Convergence Properties
We propose two line search primal-dual interior-point methods that approximately solve a equence of equality constrained barrier subproblems. To solve each subproblem, our methods apply a modified Newton method and use an $\ell_2$-exact penalty function to attain feasibility. Our methods have strong global convergence properties under standard assumptions. Specifically, if the penalty parameter remains bounded, … Read more
Extending Scope of Robust Optimization: Comprehensive Robust Counterparts of Uncertain Problems
In this paper, we propose a new methodology for handling optimization problems with uncertain data. With the usual Robust Optimization paradigm, one looks for the decisions ensuring a required performance for all realizations of the data from a given bounded uncertainty set, whereas with the proposed approach, we require also a controlled deterioration in performance … Read more
Temporal difference learning with kernels for pricing american-style options
We propose in this paper to study the problem of estimating the cost-to-go function for an infinite-horizon discounted Markov chain with possibly continuous state space. For implementation purposes, the state space is typically discretized. As soon as the dimension of the state space becomes large, the computation is no more practicable, a phenomenon referred to … Read more
Regularization Using a Parameterized Trust Region Subproblem
We present a new method for regularization of ill-conditioned problems, such as those that arise in image restoration or mathematical processing of medical data. The method extends the traditional {\em trust-region subproblem}, \TRS, approach that makes use of the {\em L-curve} maximum curvature criterion, a strategy recently proposed to find a good regularization parameter. We … Read more
On the convergence rate of the Cauchy algorithm in the l2 norm
This paper presents a convergence rate for the sequence generated by the Cauchy algorithm. The method is applied to a convex quadratic function with exact line search. Instead of using the norm induced by the hessian matrix, the q-linear convergence is shown for the l2 (or Euclidean) norm. CitationTecnhical Report, Dep. Mathematics, Federal University of … Read more
Optimal Information Monitoring Under a Politeness Constraint
We describe scheduling algorithms for monitoring an information source whose contents change at times modeled by a nonhomogeneous Poisson process. In a given time period of length T, we enforce a politeness constraint that we may only probe the source at most n times. This constraint, along with an optional constraint that no two probes … Read more