1719940
Lower bounds for approximate factorizations via semidefinite programming: (extended abstract)
The problem of approximately factoring a real or complex multivariate polynomial f seeks minimal perturbations ? f to the coefficients of the input polynomial f so that the deformed polynomial f +Δ f has the desired factorization properties. Effcient algorithms exist that compute the nearest real or complex polynomial that has non-trivial factors (see [3,6 ]and the literature cited there). Here we consider the solution of the arising optimization problems polynomial optimization (POP)via semide finite programming (SDP). We restrict to real coe cients in the input and output polynomials.
3173726
Approximate GCDs of polynomials and sparse SOS relaxations
The problem of computing approximate GCDs of several polynomials with real or complex coefficients can be formulated as computing the minimal perturbation such that the perturbed polynomials have an exact GCD of given degree. We present algorithms based on SOS (Sums Of Squares) relaxations for solving the involved polynomial or rational function optimization problems with or without constraints.
10784212
Approximate GCDs of polynomials and SOS relaxation
min p,u1,...,us ‖f1−p·u1‖2+‖f2−p·u2‖2+· · ·+‖fs−p·us‖2 (1) where p, u1, . . . , us are polynomials such that deg(p) ≤ k, deg(p · ui) ≤ di = deg fi for 1 ≤ i ≤ s. Here ‖f‖2 denotes the norm of the coefficient vector of polynomial f . The minimization problem has many different formulations and various numeric optimization strategies have been proposed, see [1, 3] and references therein. In particular, Karmarkar and Lakshman [4] proposed an algorithm based on the global minimization of a rational function to compute the approximate GCD of univariate polynomials. The most expensive part of their algorithm is to find all the real solutions of two bivariate polynomials with high degrees. It has been shown in [8] that sum of squares (SOS) relaxation[5, 9] can be used to find the global minimum of the rational function arising from the approximate GCD computation. The SOS relaxation can be solved by reformulating them as semidefinite programs (SDPs), which in turn are solved efficiently by using interior point methods [7]. Motivated by the interesting results obtained in [8], we show how to apply SOS relaxation to solve different optimization problems formulated in [1, 3, 4]. Let fi,ui,p be coefficient vectors corresponding to polynomials fi, ui, p respectively, and Ai = Ai(p) be convolution ∗ This research was partially supported by NKBRPC (2004CB318000) and the Chinese National Natural Science Foundation under Grant 10401035 (Li and Zhi).
14862024
Exact certification of global optimality of approximate factorizations via rationalizing sums-of-squares with floating point scalars
We generalize the technique by Peyrl and Parillo [Proc. SNC 2007] to computing lower bound certificates for several well-known factorization problems in hybrid symbolic-numeric computation. The idea is to transform a numerical sum-of-squares (SOS) representation of a positive polynomial into an exact rational identity. Our algorithms successfully certify accurate rational lower bounds near the irrational global optima for benchmark approximate polynomial greatest common divisors and multivariate polynomial irreducibility radii from the literature, and factor coefficient bounds in the setting of a model problem by Rump (up to n = 14, factor degree = 13.
 The numeric SOSes produced by the current fixed precision semi-definite programming (SDP) packages (SeDuMi, SOSTOOLS, YALMIP) are usually too coarse to allow successful projection to exact SOSes via Maple 11's exact linear algebra. Therefore, before projection we refine the SOSes by rank-preserving Newton iteration. For smaller problems the starting SOSes for Newton can be guessed without SDP ("SDP-free SOS"), but for larger inputs we additionally appeal to sparsity techniques in our SDP formulation.
16772027
CCL-SVC: Optimizing user experience of broadcasting video on computation capability limited handheld devices
In this paper, we propose a novel scheme using computing complexity layered scalable video coding (CCLSVC) to optimize the user experience of broadcasting video in the computing capability limited handheld terminals. To address the heterogeneity of computing capability among different handheld devices, we employ hierarchal B reference structure of SVC to divide the frames into multiple computing complexity layers (CC Layers) in server side. The handheld clients simply choose to decode the frames in their corresponding layers in terms of their computation capability to maximize the video PSNR. We have proved that the optimal CC Layers division problem is a precedence constrained scheduling problem, which is an NP-complete problem. And we further propose our fast greedy method to approximately get optimized broadcasting video playback PSNR. The simulation shows that our method is superior to temporal SVC and random frame discarding method.
29843270
A Self-adaptive Mixed Distribution Based Uni-variate Estimation of Distribution Algorithm for Large Scale Global Optimization
Large scale global optimization (LSGO), which is highly needed for many scientific and engineering applications, is a very important and very difficult task in optimization domain. Various algorithms have been proposed to tackle this challenging problem, but the use of estimation of distribution algorithms (EDAs) to it is rare. This chapter aims at investigating the behavior and performances of uni-variate EDAs mixed with different kernel probability densities via fitness landscape analysis. Based on the analysis, a self-adaptive uni-variate EDA with mixed kernels (MUEDA) is proposed. To assess the effectiveness and efficiency of MUEDA, function optimization tasks with dimension scaling from 30 to 1500 are adopted. Compared to the recently published LSGO algorithms, MUEDA shows excellent convergence speed, final solution quality and dimensional scalability.
7375220
Dynamic User Modeling for Sketch-Based User Interface
This paper presents a strategy of dynamic user modeling for sketch-based user interface. A user model is defined as an incremental decision tree for a specific user. A drawing style modeling process is designed to model user's temporal drawing performances among inputting strokes, and to predict the possible shape in term of fuzzy matching. A user mediation process is proposed based on relevance feedback to capture users' drawing intentions and refine the recognition results. Experiments prove efficiency of the method.
2854723
UTDallas at TREC 2008 Blog Track
Abstract : This paper describes our participation in the 2008 TREC Blog track. Our system consists of 3 components: data preprocessing, topic retrieval, and opinion finding. In the topic retrieval task, we applied Lemur IR toolkit and used various techniques for query expansion. In the opinion finding and polarization task, we employed a feature-based classification approach. Then re-ranking was performed using a linear combination of the opinionated score and the topic relevance score. Our system achieved reasonable performance in this evaluation.
15998088
Understand behavior and performance of Real Coded Optimization Algorithms via NK-linkage model
Classical NK-landcape model was designed for analyzing optimization and evolution process in binary solution space, so it can not be used to analyze real coded optimization algorithms (RCOAs) directly, which work in continuous solution space directly. In this paper, the concept of NK-landscape model is extended to the continuous space, and a new NK-landscape model with continuous space is proposed. The new model is powerful and comprehensive with simple structure and flexible formula. Therefore, it can be used to construct test functions of various types of linkages for analyzing various performances of RCOAs. The feasibility of the proposed model is testified via experiments with 3 well-known RCOAs, ( i.e. covariance matrix adapting evolutionary strategy (CMA-ES), differential evolution (DE), neighborhood search differential evolution (NSDE)). The results show that the new model can reveal the merits and demerits of RCOAs effectively.