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.
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.
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.
7717414
A time interval based consistency control algorithm for interactive groupware applications
Traditional concurrency control methods such as locking and serialization are not suitable for distributed interactive applications that demand fast local response. Operational transformation (OT) is the standard solution to concurrency control and consistency maintenance in group editors, an important class of interactive groupware applications. It generally trades consistency for local responsiveness, because human users can often tolerate temporary inconsistencies but do not like their interactions be lost or nondeterministically blocked. This paper presents a time interval based operational transformation algorithm (TIBOT) that overcomes the various limitations of previous related work. Our approach guarantees content convergence and is significantly more simple and efficient than existing approaches. This is achieved in a pure replicated architecture by using a linear clock and by posing some constraints on communication that are reasonable for the application domain.
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.
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.
17329223
Supereulerian planar graphs
We investigate the supereulerian graph problems within planar graphs, and we prove that if a 2-edge-connected planar graph G is at most three edges short of having two edge-disjoint spanning trees, then G is supereulerian except a few classes of graphs. This is applied to show the existence of spanning Eulerian subgraphs in planar graphs with small edge cut conditions. We also determine several extremal bounds for planar graphs to be supereulerian.
7985665
Eulerian subgraphs and Hamilton-connected line graphs
Let C(l,k) denote a class of 2-edge-connected graphs of order n such that a graph G ∈ C(l,k) if and only if for every edge cut S ⊆ E(G) with |S| ≤ 3, each component of G-S has order at least (n-k)/l. We prove the following: (1) If G ∈ C(6,0), then G is supereulerian if and only if G cannot be contracted to K2,3, K2,5 or K2,3(e), where e ∈ E(K2,3) and K2,3(e) stands for a graph obtained from K2,3 by replacing e by a path of length 2. (2) If G ∈ C(6, 0) and n≥7, then L(G) is Hamilton-connected if and only if κ(L(G))≥3. Former results by Catlin and Li, and by Broersma and Xiong are extended.