A method is presented that automatically improves upon previous treatment plans by optimization under reference dose constraints. In such an optimization, a previous plan is taken as reference and a new optimization is performed towards some goal, such as minimization of the doses to healthy structures, under the constraint that no structure can become worse … Read more
This paper describes a new approach for computing nonnegative matrix factorizations (NMFs) with linear programming. The key idea is a data-driven model for the factorization, in which the most salient features in the data are used to express the remaining features. More precisely, given a data matrix X, the algorithm identifies a matrix C that … Read more
We consider the convex feasibility problem (CFP) in Hilbert space and concentrate on the study of string-averaging projection (SAP) methods for the CFP, analyzing their convergence and their perturbation resilience. In the past, SAP methods were formulated with a single predetermined set of strings and a single predetermined set of weights. Here we extend the … Read more
Many real-world dynamic problems have constraints, and in certain cases not only the objective function changes over time, but also the constraints. However, there is no research in answering the question of whether current algorithms work well on continuous dynamic constrained optimisation problems (DCOPs), nor is there any benchmark problem that reflects the common characteristics … Read more
In many applications, the discretization of continuous ill-posed inverse problems results in discrete ill-posed problems whose solution requires the use of regularization strategies. The L-curve criterium is a popular tool for choosing good regularized solutions, when the data noise norm is not a priori known. In this work, we propose replacing the original ill-posed inverse … Read more
We consider a time-optimal problem for the Reeds and Shepp model describing a moving point on a plane, with a onesided variation of the speed and a free final direction of velocity. Using Pontryagin Maximum Principle, we obtain all possible types of extremals and, analyzing them and discarding nonoptimal ones, construct the optimal synthesis. Citation … Read more
pcaL1 is a package for the R environment for finding principal components using methods based on the L1 norm. The principal components derived using traditional principal component analysis (PCA) can be interpreted as an optimal solution to several optimization problems involving the L2 norm. Using the L1 norm in these problems provides an alternative that … Read more
In this paper we discuss two particular layout problems, namely the Single-Row Equidistant Facility Layout Problem (SREFLP) and the Single-Row Facility Layout Problem (SRFLP). Our aim is to consolidate the two respective branches in the layout literature. We show that the SREFLP is not only a special case of the Quadratic Assignment Problem but also … Read more
This paper proposes a new algorithm for linear system identification from noisy measurements. The proposed algorithm balances a data fidelity term with a norm induced by the set of single pole filters. We pose a convex optimization problem that approximately solves the atomic norm minimization problem and identifies the unknown system from noisy linear measurements. … Read more
The sub-Nyquist estimation of line spectra is a classical problem in signal processing, but currently popular subspace-based techniques have few guarantees in the presence of noise and rely on a priori knowledge about system model order. Motivated by recent work on atomic norms in inverse problems, we propose a new approach to line spectral estimation … Read more