46474884
Explicit Efficient Frontier of a Continuous-Time Mean Variance Portfolio Selection Problem
In this work we consider a continuous-time mean-variance portfolio selection problem that is formulated as a bi-criteria optimization problem. The objective is to maximize the expected return and minimize the variance of the terminal wealth. By putting weights on the two criteria one obtains a single objective stochastic control problem which is however not in the standard form. We show that this non-standard problem can be “embedded” into a class of auxiliary stochastic linear-quadratic (LQ) problems. By solving the latter based on the recent development on stochastic LQ problems with indefinite control weighting matrices, we derive the efficient frontier in a closed form for the original mean-variance problem.
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.
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.
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.
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.
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.
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.
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.
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.
5115871
Temporal Knowledge Discovery with Infrequent Episodes
In this paper, we present an efficient algorithm which discovers rare episodes with a combination of bottom-up and top-down scanning schema. The information sharing between bottom-up and top-down scannings helps prune candidate episodes, and thus, efficiently find infrequent episodes that are interesting to user: We evaluate the performance of the algorithm using real-life weather databases. We observe from experimental results that our approach results in 30%-90% reduction in computation time and 25%-75% reduction in the number of candidates comparing with Apriori algorithm.