We model a dependency graph as a book, a particular kind of topological space, for semantic dependency parsing. The spine of the book is made up of a sequence of words, and each page contains a subset of noncrossing arcs. To build a semantic graph for a given sentence, we design new Maximum Subgraph algorithms to generate noncrossing graphs on each page, and a Lagrangian Relaxation-based algori...

We consider a broad class of stochastic dynamic programming problems that are amenable to relaxation via decomposition. These problems comprise multiple subproblems that are independent of each other except for a collection of coupling constraints on the action space. We fit an additively separable value function approximation using two techniques, namely, Lagrangian relaxation and the linear p...

We present a row-by-row (RBR) method for solving semidefinite programming (SDP) problem based on solving a sequence of problems obtained by restricting the n-dimensional positive semidefinite constraint on the matrix X. By fixing any (n − 1)-dimensional principal submatrix of X and using its (generalized) Schur complement, the positive semidefinite constraint is reduced to a simple second-order...

The economical determination of lot size with capacity constraints is a frequently complex, problem in the real world. In this paper, a multi-level problem of lotsizing with capacity constraints in a finite planning horizon is investigated. A combination of ant colony algorithm and a heuristic method called shifting technique is proposed for solving the problem. The parameters, including the co...

In this paper, we consider solution approaches to a multihour combined capacity design and routing problem which arises in the design of dynamically reconfigurable broadband communication networks that uses the virtual path concept. We present a comparative evaluation of four approaches, namely: a genetic algorithm, a Lagrangian relaxation based subgradient optimization method, a generalized pr...

In this research, we develop an integrated scheduling model that combines passenger, cargo and combi flight scheduling. We employ network flow techniques to construct the model which is formulated as an integer multiple commodity network flow problem that is characterized as NP-hard. A family of heuristics, based on Lagrangian relaxation, a sub-gradient method, heuristics for the upper bound so...

In this paper, we address the rate control problem for layered multicast sessions, with the objective of solving a generalized throughput/fairness objective. Our approach is based on a combination of Lagrangian relaxation and dynamic programming. Unlike previously proposed dual-based approaches, the algorithm presented in this paper scales well as the number of multicast sessions in the network...

Decomposition algorithms such as Lagrangian relaxation and Dantzig-Wolfe decomposition are well-known methods that can be used to compute bounds for integer programming problems. We discuss a framework for integrating dynamic cut generation with traditional decomposition methods in order to obtain improved bounds and present a new paradigm for separation called decompose and cut. The methods we...