30170890
A new algorithm for generalized fractional programs
A new dual problem for convex generalized fractional programs with no duality gap is presented and it is shown how this dual problem can be efficiently solved using a parametric approach. The resulting algorithm can be seen as “dual” to the Dinkelbach-type algorithm for generalized fractional programs since it approximates the optimal objective value of the dual (primal) problem from below. Convergence results for this algorithm are derived and an easy condition to achieve superlinear convergence is also established. Moreover, under some additional assumptions the algorithm also recovers at the same time an optimal solution of the primal problem. We also consider a variant of this new algorithm, based on scaling the “dual” parametric function. The numerical results, in case of quadratic-linear ratios and linear constraints, show that the performance of the new algorithm and its scaled version is superior to that of the Dinkelbach-type algorithms. From the computational results it also appears that contrary to the primal approach, the “dual” approach is less influenced by scaling.
14478113
Sequencing jobs that require common resources on a single machine: A solvable case of the TSP
In this paper a one-machine scheduling model is analyzed wheren different jobs are classified intoK groups depending on which additional resource they require. The change-over time from one job to another consists of the removal time or of the set-up time of the two jobs. It is sequence-dependent in the sense that the change-over time is determined by whether or not the two jobs belong to the same group. The objective is to minimize the makespan. This problem can be modeled as an asymmetric Traveling Salesman Problem (TSP) with a specially structured distance matrix. For this problem we give a polynomial time solution algorithm that runs in O(n logn) time. © 1998 The Mathematical Programming Society, Inc. Published by Elsevier Science B.V.
16330147
A Primal-Dual Decomposition Algorithm for Multistage Stochastic Convex Programming
This paper presents a new and high performance solution method for multistage stochastic convex programming. Stochastic programming is a quantitative tool developed in the field of optimization to cope with the problem of decision-making under uncertainty. Among others, stochastic programming has found many applications in finance, such as asset-liability and bond-portfolio management. However, many stochastic programming applications still remain computationally intractable because of their overwhelming dimensionality. In this paper we propose a new decomposition algorithm for multistage stochastic programming with a convex objective and stochastic recourse matrices, based on the path-following interior point method combined with the homogeneous self-dual embedding technique. Our preliminary numerical experiments show that this approach is very promising in many ways for solving generic multistage stochastic programming, including its superiority in terms of numerical efficiency, as well as the flexibility in testing and analyzing the model.
12742018
On Cones of Nonnegative Quadratic Functions
We derive linear matrix inequality (LMI) characterizations and dual decomposition algorithms for certain matrix cones which are generated by a given set using generalized co-positivity. These matrix cones are in fact cones of nonconvex quadratic functions that are nonnegative on a certain domain. As a domain, we consider for instance the intersection of a (upper) level-set of a quadratic function and a half-plane. Consequently, we arrive at a generalization of Yakubovich's S-procedure result. Although the primary concern of this paper is to characterize the matrix cones by LMIs, we show, as an application of our results, that optimizing a general quadratic function over the intersection of an ellipsoid and a half-plane can be formulated as semidefinite programming (SDP), thus proving the polynomiality of this class of optimization problems, which arise, e.g., from the application of the trust region method for nonlinear programming. Other applications are in control theory and robust optimization.
3196759
Low-complexity algorithms for sequencing jobs with a fixed number of job-classes
In this paper we consider the problem of scheduling n jobs such that makespan is minimized. It is assumed that the jobs can be divided into K job-classes and that the change-over time between two consecutive jobs depends on the job-classes to which the two jobs belong. In this setting, we discuss the one machine scheduling problem with arbitrary processing times and the parallel machines scheduling problem with identical processing times. In both cases it is assumed that the number of job-classes K is fixed. By using an appropriate integer programming formulation with a fixed number of variables and constraints, it is shown that these two problems are solvable in polynomial time. For the one machine scheduling case it is shown that the complexity of our algorithm is linear in the number of jobs n. Moreover, if the problem is encoded according to the high multiplicity model of Hochbaum and Shamir, the time complexity of the algorithm is shown to be a polynomial in log n. In the parallel machine scheduling case, it is shown that if the number of machines is fixed the same results hold.
17355776
A deep cut ellipsoid algorithm for convex programming: Theory and applications
This paper proposes a deep cut version of the ellipsoid algorithm for solving a general class of continuous convex programming problems. In each step the algorithm does not require more computational effort to construct these deep cuts than its corresponding central cut version. Rules that prevent some of the numerical instabilities and theoretical drawbacks usually associated with the algorithm are also provided. Moreover, for a large class of convex programs a simple proof of its rate of convergence is given and the relation with previously known results is discussed. Finally some computational results of the deep and central cut version of the algorithm applied to a min—max stochastic queue location problem are reported.
17630030
Prediction of Protein Complexes Based on Protein Interaction Data and Functional Annotation Data Using Kernel Methods
Prediction of protein complexes is a crucial problem in computational biology. The increasing amount of available genomic data can enhance the identification of protein complexes. Here we describe an approach for predicting protein complexes based on integration of protein-protein interaction (PPI) data and protein functional annotation data. The basic idea is that proteins in protein complexes often interact with each other and protein complexes exhibit high functional consistency/even multiple functional consistency. We create a protein-protein relationship network (PPRN) via a kernel-based integration of these two genomic data. Then we apply the MCODE algorithm on PPRN to detect network clusters as numerically determined protein complexes. We present the results of the approach to yeast Sacchromyces cerevisiae. Comparison with well-known experimentally derived complexes and results of other methods verifies the effectiveness of our approach.
5567441
Compacting XML Data
Compression aims to reduce the size of data without loss of information. Compaction is a special kind of compression in which the output is in the same language as the input. Compaction of an XML data forest produces a smaller XML forest, without losing any data. This paper develops a formal framework for the compaction of XML data and presents two compaction techniques.
6437552
Heavy paths and cycles in weighted graphs
A weighted graph is a graph in which each edge is assigned a non-negative number, called the weight. The weight of a path (cycle) is the sum of the weights of its edges. The weighted degree of a vertex is the sum of the weights of the edges incident with the vertex. A usual (unweighted) graph can be considered as a weighted graph with constant weight 1. In this paper, it is proved that for a 2-connected weighted graph, if every vertex has weighted degree at least d, then for any given vertex y, either y is contained in a cycle with weight at least 2d or every heaviest cycle is a Hamilton cycle. This result is a common generalization of Grotschel's theorem and Bondy–Fan's theorem assuring the existence of a cycle with weight at least 2d on the same condition. Also, as a tool for proving this result, we show a result concerning heavy paths joining two specific vertices and passing through one given vertex.
29457354
A novel shape matching method using biological sequence dynamic alignment
Shape description and its corresponding matching algorithm is one of the main concerns in MPEG-7. A novel dynamic shape matching algorithm is proposed. First, the conventional 8-directional chain code is exploited to describe the binary shape. A dynamic shape matching algorithm, which is derived from the solution for the biological sequence similarity analysis based on molecular evolutionary theory, is proposed to measure the similarity distance between the shapes by computing their similarity score (SS). Based on a large set of MPEG-7 binary shapes, simulation results have shown that the proposed dynamic alignment matching algorithm is fairly promising and also robust to scale changes, small non-rigid deformation, and similarity based shape matching defined in MPEG-7 core experiments.
9519800
Turbulent Decay and Mixing of Accelerated Inhomogeneous Flows Via a Feature Based Analysis
In this paper, we focus on the late time turbulence of an accelerated inhomogeneous flow environment, which is a generalization of the Richtmyer--Meshkov environment. The numerical investigation is based on two-dimensional (2D) compressible Euler simulation, which is initiated by a shock wave hitting a gas layer (curtain). Although our unforced study is based on the intrinsic numerical dissipation, we observe excellent agreement with the previous decay analysis on 2D viscous isotropic homogeneous turbulence at inertial range [J. R. Chasnov, Phys. Fluids, 9 (1997), pp. 171--180]. The baroclinic circulation in our environment plays a major role in the mass transport and mixing. The mass-transport induced density gradient intensification, in turn, enhances the circulation baroclinically and provides an intrinsic forcing at intermediate to high wave number range. With the assistance of a computer graphics based feature extraction and tracking algorithm, we address quantitatively the spatial and temporal diffusivity of the mixing zone. We study and compare both the slow/fast/slow and fast/slow/fast cases to illustrate heuristically the correlation of mass and momentum diffusivity.