2989522
Zero duality gap in integer programming: P-norm surrogate constraint method
A p-norm surrogate constraint method is proposed for integer programming. A single surrogate constraint can be always constructed using a p-norm such that the feasible sets in a surrogate relaxation and the primal problem match exactly. The p-norm surrogate constraint method is thus guaranteed to succeed in identifying an optimal solution of the primal problem with zero duality gap. The existence of a saddle point is proven for integer programming problems.
36670641
A nonlinear Lagrangian dual for integer programming
Nonlinear Lagrangian theory offers a success guarantee for the dual search via construction of a nonlinear support of the perturbation function at the optimal point. In this paper, a new nonlinear dual formulation of an exponential form is proposed for bounded integer programming. This new formulation possesses an asymptotic strong duality property and guarantees a success in identifying a primal optimum solution. No actual dual search is needed in the solution process when the parameter of the nonlinear Lagrangian formulation is set to be large enough.
207726898
Quick response policy with Bayesian information updates
Abstract In this paper we investigate the quick response (QR) policy with different Bayesian models. Under QR policy, a retailer can collect market information from the sales of a pre-seasonal product whose demand is closely related to a seasonal product’s demand. This information is then used to update the distribution for the seasonal product’s demand by a Bayesian approach. We study two information update models: one with the revision of an unknown mean, and the other with the revision of both an unknown mean and an unknown variance. The impacts of the information updates under both models are compared and discussed. We also identify the features of the pre-seasonal product which can bring more significant profit improvement. We conclude that an effective QR policy depends on a precise information update model as well as a selection of an appropriate pre-seasonal product as the observation target.
27085223
Normal vector identification and interactive tradeoff analysis using minimax formulation in multiobjective optimization
In multiobjective optimization, tradeoff analysis plays an important role in determining the best search direction to reach a most preferred solution. This paper presents a new explicit interactive tradeoff analysis method based on the identification of normal vectors on a noninferior frontier. The interactive process is implemented using a weighted minimax formulation by regulating the relative weights of objectives in a systematic manner. It is proved under a mild condition that a normal vector can be identified using the weights and Kuhn-Tucker (K-T) multipliers in the minimax formulation. Utility gradients can be estimated using local preference information such as marginal rates of substitution. The projection of a utility gradient onto a tangent plane of the noninferior frontier provides a descent direction of disutility and thereby a desirable tradeoff direction, along which tradeoff step sizes can be decided by the decision maker using an explicit tradeoff table. Necessary optimality conditions are established in terms of normal vectors and utility gradients, which can be used to guide the elicitation of local preferences and also to terminate an interactive process in a rigorous yet flexible way. This method is applicable to both linear and nonlinear (either convex or nonconvex) multiobjective optimization problems. Numerical examples are provided to illustrate the theoretical results of the paper and the implementation of the proposed interactive decision analysis process.
7454095
On the relationship between the integer and continuous solutions of convex programs
Abstract A bound is obtained in this note for the distance between the integer and real solutions to convex quadratic programs. This bound is a function of the condition number of the Hessian matrix. We further extend this proximity result to convex programs and mixed-integer convex programs. We also show that this bound is achievable in certain situations and the distance between the integer and continuous minimizers may tend to infinity.
19454602
Asymptotic Strong Duality for Bounded Integer Programming: A Logarithmic-Exponential Dual Formulation
A logarithmic-exponential dual formulation is proposed in this paper for bounded integer programming problems. This new dual formulation possesses an asymptotic strong duality property and guarantees the identification of an optimal solution of the primal problem. These prominent features are achieved by exploring a novel nonlinear Lagrangian function, deriving an asymptotic zero duality gap, investigating the unimodality of the associated dual function and ensuring the primal feasibility of optimal solutions in the dual formulation. One other feature of the logarithmicexponential dual formulation is that no actual dual search is needed when parameters are set above certain threshold-values.
15275424
Blur identification based on kurtosis minimization
In this paper, we describe an algorithm for identifying a parametrically described blur based on kurtosis minimization. Using different choices for the parameters of the blur, the noisy blurred image is restored using Wiener filter. We use the kurtosis as a measurement of the quality of the restored image. From the set of the candidate deblurred images, the one with the minimum kurtosis is selected. The proposed technique is tested in a simulated experiment on a variety of blurs including atmospheric turbulence blurs, Gaussian blurs, and out-of-focus blurs. The proposed approach is also tested on real blurred images. Moreover, we test the performance when a wrong blur model is given. Our experiments show that the kurtosis minimization measurements match well with methods that maximize PSNR.
17504688
A statistical method for binary classification of images
The classification of documents with sparse text, and video analysis, relies on accurate image classification. We herein present a method for binary classification that accommodates any number of individual classifiers. Each individual classifier is defined by the critical point between its two means, and its relative weighting is inversely proportional to its expected error rate. Using 10 simple image analysis metrics, we distinguish a set of "natural" and "city" scenes, providing a "semantically meaningful" classification. The optimal combination of 5 of these 10 classifiers provides 85.8% accuracy on a small (120 image) feasibility corpus. When this feasibility corpus is then split into half training and half testing images, the mean accuracy of the optimum set of classifiers was 81.7%. Accuracy as high as 90% was obtained for the test set when training percentage was increased. These results demonstrate that an accurate classifier can be constructed from a large pool of simple classifiers through the use of the statistical ("Normal") classification method described herein.
6337639
Transparent sharing and interoperation of heterogeneous single-user applications
Multi-user applications generally lag behind in features or compatibility with single-user applications. As a result, users are often not motivated to abandon their favorite single-user applications for groupware features that are less frequently used. A well-accepted approach, collaboration transparency, is able to convert off-the-shelf single-user applications into groupware without modifying the source code. However, existing systems have been largely striving to develop generic application-sharing mechanisms and undesirably force users to share the same application in cooperative work. In this paper we analyze this problem and present a novel approach (called intelligent collaboration transparency) to addressing this problem. Our approach allows for heterogeneous application sharing by considering the particular semantics of the applications and the collaboration task in question.
8785272
A Framework for Building Collaboration Tools by Leveraging Industrial Components
Groupware applications allow a distributed group of human users to work apart together over a computer network They are difficult to develop due to the needs to suit a range of collaboration tasks that are often with diverse and evolutionary requirements To address this problem, we propose a new framework in which shared data components conforming to a well-defined interface can be dynamically plugged in for flexible sharing, and a simple transformation tool is provided such that the myriad of industrial collaboration-transparent components can be transformed into shared components The validity of our framework is evaluated by building a suite of typical collaboration tools such as group editors Under our framework, most components in the Java Development Kit (JDK) can be transformed automatically for prototyping collaboration tools With minimal manual work, those tools can be adapted to achieve advanced flexibility, e.g., data and control components can be bound dynamically to switch control protocols.
669815
Modified linear discriminant analysis
In this paper, a modified Fisher linear discriminant analysis (FLDA) is proposed and aims to not only overcome the rank limitation of FLDA, that is, at most only finding a discriminant vector for 2-class problem based on Fisher discriminant criterion, but also relax singularity of the within-class scatter matrix and finally improves classification performance of FLDA. Experiments on nine publicly available datasets show that the proposed method has better or comparable performance on all the datasets than FLDA.