Service System Design in the Public and Private Sectors
abstract CitationIn Proceeding of the International Conference: Mathematical Methods in Economics, Virt 2004, pp. 101-108, ISBN 80-8078-012-9ArticleDownload View PDF
Relaxing the Optimality Conditions of Box QP
We present semidefinite relaxations of nonconvex, box-constrained quadratic programming, which incorporate the first- and second-order necessary optimality conditions. We compare these relaxations with a basic semidefinite relaxation due to Shor, particularly in the context of branch-and-bound to determine a global optimal solution, where it is shown empirically that the new relaxations are significantly stronger. We … Read more
Sparse Reconstruction by Separable Approximation
Finding sparse approximate solutions to large underdetermined linear systems of equations is a common problem in signal/image processing and statistics. Basis pursuit, the least absolute shrinkage and selection operator (LASSO), wavelet-based deconvolution and reconstruction, and compressed sensing (CS) are a few well-known areas in which problems of this type appear. One standard approach is to … Read more
Enclosing Machine Learning
This report introduces a new machine learning paradigm called enclosing machine learning for data mining. This novel method utilizes the virtues of human being’s cognition process and tries to imitate the two basic principles of cognition process from a macroscopical view, which are cognizing things of the same kind, recognizing things of a new kind … Read more
Combining segment generation with direct step-and-shoot optimization in intensity-modulated radiation therapy
A method for generating a sequence of intensity-modulated radiation therapy step-and-shoot plans with increasing number of segments is presented. The objectives are to generate high-quality plans with few, large and regular segments, and to make the planning process more intuitive. The proposed method combines segment generation with direct step-and-shoot optimization, where leaf positions and segment … Read more
Sufficient and Necessary Conditions for Semidefinite Representability of Convex Hulls and Sets
The article proves sufficient conditions and necessary conditions for SDP representability of convex sets and convex hulls by proposing a new approach to construct SDP representations. The contributions of this paper are: (i) For bounded SDP representable sets $W_1,\cdots,W_m$, we give an explicit construction of an SDP representation for $conv(\cup_{k=1}^mW_k)$. This provides a technique for … Read more
A Numerical Algorithm for Block-Diagonal Decomposition of Matrix *-Algebras, Part I: Proposed Approach and Application to Semidefinite Programming
Motivated by recent interest in group-symmetry in semidefinite programming, we propose a numerical method for finding a finest simultaneous block-diagonalization of a finite number of matrices, or equivalently the irreducible decomposition of the generated matrix *-algebra. The method is composed of numerical-linear algebraic computations such as eigenvalue computation, and automatically makes full use of the … Read more
Bracketing an Optima in Univariate Optimization
In this article, we consider some problems of bracketing an optimum point for a real-valued, single variable function. We show that, no method, satisfying certain assumptions and requiring a bounded number of function evaluations, can exist to bracket the minimum point of a unimodal function. A similar result is given also for the problem of … Read more
Regularization methods for semidefinite programming
This paper studies an alternative technique to interior point methods and nonlinear methods for semidefinite programming (SDP). The approach based on classical quadratic regularizations leads to an algorithm, generalizing a recent method called “boundary point method”. We study the theoretical properties of this algorithm and we show that in practice it behaves very well on … Read more
A multilevel algorithm for solving the trust-region subproblem
We present a multilevel numerical algorithm for the exact solution of the Euclidean trust-region subproblem. This particular subproblem typically arises when optimizing a nonlinear (possibly non-convex) objective function whose variables are discretized continuous functions, in which case the different levels of discretization provide a natural multilevel context. The trust-region problem is considered at the highest … Read more