Fitting piecewise affine models to data points is a pervasive task in many scientific disciplines. In this work, we address the k- Piecewise Affine Model Fitting with Pairwise Linear Separability problem (k-PAMF-PLS) where, given a set of real points and the corresponding observations, we have to partition the real domain into k pairwise linearly separable … Read more
Applications in engineering frequently require the adjustment of certain parameters. While the mathematical laws that determine these parameters often are well understood, due to time limitations in every day industrial life, it is typically not feasible to derive an explicit computational procedure for adjusting the parameters based on some given measurement data. This paper aims … Read more
Many idealized problems in signal processing, machine learning and statistics can be reduced to the problem of finding the symmetric canonical decomposition of an underlying symmetric and orthogonally decomposable (SOD) tensor. Drawing inspiration from the matrix case, the successive rank-one approximations (SROA) scheme has been proposed and shown to yield this tensor decomposition exactly, and … Read more
When considering cost-optimal operation of gas transport networks, compressor stations play the most important role. Proper modeling of these stations leads to complicated mixed-integer nonlinear and nonconvex optimization problems. In this article, we give an isothermal and stationary description of compressor stations, state MINLP and GDP models for operating a single station, and discuss several … Read more
Experience and observations often underlie some widely used numerical characteristics. The problem is in the extent to which such characteristics are optimal. The paper presents results of theoretical analysis of the most frequently used numerical characteristics regarding the number of classes in classification systems, of the base of the number system, and of the level … Read more
We develop an optimization technique to compute local solutions to synthesis problems subject to integral quadratic constraints (IQCs). We use the fact that IQCs may be transformed into semi-infinite maximum eigenvalue constraints over the frequency axis and approach them via nonsmooth optimization methods. We develop a suitable spectral bundle method and prove its convergence in … Read more
We investigate the application of the nonmonotone spectral projected gradient (SPG) method to a region-based variational model for image segmentation. We consider a “discretize-then-optimize” approach and solve the resulting nonlinear optimization problem by an alternating minimization procedure that exploits the SPG2 algorithm by Birgin, Martìnez and Raydan (SIAM J. Optim., 10(4), 2000). We provide a … Read more
In this paper we study the convex problem of optimizing the sum of a smooth function and a compactly supported non-smooth term with a specific separable form. We analyze the block version of the generalized conditional gradient method when the blocks are chosen in a cyclic order. A global sublinear rate of convergence is established … Read more
We investigate the multi-dimensional Super Resolution problem on closed semi-algebraic domains for various sampling schemes such as Fourier or moments. We present a new semidefinite programming (SDP) formulation of the l1-minimization in the space of Radon measures in the multi-dimensional frame on semi-algebraic sets. While standard approaches have focused on SDP relaxations of the dual … Read more
In this paper, we propose a new step size rule to accelerate Yan et al.’s self-adaptive projection method. Under the new step size strategy, the superiority of modified projection method is verified through theory to numerical experiments. Citation College of Communications Engineering, PLA University of Science and Technology, Nanjing, 210007, China 01/29/2015 Article Download View … Read more