1427576
On a New Homotopy Continuation Trajectory for Nonlinear Complementarity Problems
Most known continuation methods for P 0 complementarity problems require some restrictive assumptions, such as the strictly feasible condition and the properness condition, to guarantee the existence and the boundedness of certain homotopy continuation trajectory. To relax such restrictions, we propose a new homotopy formulation for the complementarity problem based on which a new homotopy continuation trajectory is generated. For P 0 complementarity problems, the most promising feature of this trajectory is the assurance of the existence and the boundedness of the trajectory under a condition that is strictly weaker than the standard ones used widely in the literature of continuation methods. Particularly, the often-assumed strictly feasible condition is not required here. When applied to P * complementarity problems, the boundedness of the proposed trajectory turns out to be equivalent to the solvability of the problem, and the entire trajectory converges to the (unique) least element solution provided that it exists. Moreover, for monotone complementarity problems, the whole trajectory always converges to a least 2-norm solution provided that the solution set of the problem is nonempty. The results presented in this paper can serve as a theoretical basis for constructing a new path-following algorithm for solving complementarity problems, even for the situations where the solution set is unbounded.
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.
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.
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.
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.
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.
4669631
A new hierarchical control scheme for a class of cyclically repeated discrete-event systems
We extend the hierarchical control method in (Li et al., 2004) to a more generic setting which involves cyclically repeated processes. A hierarchical architecture is presented to facilitate control synthesis. Specifically, a conservative max-plus model for cyclically repeated processes is introduced on the upper level which provides an optimal online plan list. An enhanced min-plus algebra based scheme on the lower level not only handles unexpected events but, more importantly, addresses cooperation issues between sub-plants and different cycles. A rail traffic example is given to demonstrate the effectiveness of the proposed approach.
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.
1387834
An Efficient Algorithm for Pattern Discovery in Large Text Databases
1850331
COCA: collaborative objects coordination architecture
Coordination policies vary from collaboration to collaboration and are even subject to evolution in different phases of the same collaboration. It is vital for collaborative systems to be flexible enough to accommodate changes to the coordination policies du ring development and the lifetime of the collaboration. Motivated by previous work of separating coordinati on and computation, we propose COCA as a generic framework for developing collaborative systems and modeling the coordination policies. Participants ex plicitly adopt roles, and coordination policies are specifie d in terms of roles in a logic-based specification langu age. Policies are interpreted at runtime at each collabo r ti n site by a COCA virtual machine. It is easy to chang e the coordination policies both during development and a t runtime.