This paper presents the design of a novel distributed algorithm d-IRA for the reachability analysis of linear hybrid automata. Recent work on iterative relaxation abstraction (IRA) is leveraged to distribute the reachability problem among multiple computational nodes in a non-redundant manner by performing careful infeasibility analysis of linear programs corresponding to spurious counterexampl...

In this note we show that Ye-Todd-Mizuno's O(p nL)-iteration homogeneous and self-dual linear programming (LP) algorithm possesses quadratic convergence of the duality gap to zero. In the case of infeasibility, this result shows that a homogenizing variable quadratically converges to zero and implies that the iterates of the (original) LP variable quadratically diverge. Thus, we have establishe...

We show that a modiication of the combined Phase I-Phase II interior-point algorithm for linear programming, due to Anstreicher, de Ghellinck and Vial, Fra-ley, and Todd, terminates in O(p nL) iterations from a suitable initial (interior but infeasible) solution. The algorithm either detects infeasibility, or approaches feasibility and optimality simultaneously, or generates a feasible primal-d...

A filter algorithm with inexact line search is proposed for solving nonlinear programming problems. The filter is constructed by employing the norm of the gradient of the Lagrangian function to the infeasibility measure. Transition to superlinear local convergence is showed for the proposed filter algorithm without second-order correction. Under mild conditions, the global convergence can also ...

Deniable authentication protocol enables a receiver to identify the true source of a given message, but not to prove the identity of the sender to a third party. This property is very useful for providing secure negotiation over the Internet. This paper describes a secure identity based deniable authentication protocol whose security is based on computational infeasibility of solving DiffieHell...

What sets SAT apart from other combinatorial optimization problems is that SAT is basically a feasibility problem. Once a variable assignment is found that satisfies all the clauses (see Section 2), the problem is solved. There is thus no guidance from the objective function. Guidance is customarily instead based on the amount of infeasibility, usually by counting the number of unsatisfied clau...

Knapsack constraints are a key modeling structure in constraint programming. These constraints are normally handled with simple bounding arguments. We propose a dynamic programming structure to represent these constraints. With this structure, we are able to achieve hyper-arc consistency, to determine infeasibility before all variables are set, to generate all solutions quickly, and to provide ...

We propose a very simple preprocessing algorithm for semidefinite programming. Our algorithm inspects the constraints of the problem, deletes redundant rows and columns in the constraints, and reduces the size of the variable matrix. It often detects infeasibility. Our algorithm does not rely on any optimization solver: the only subroutine it needs is Cholesky factorization, hence it can be imp...

We present a new strategy for choosing primal and dual steplengths in a primal-dual interior-point algorithm for convex quadratic programming. Current implementations often scale steps equally to avoid increases in dual infeasibility between iterations. We propose that this method can be too conservative, while safeguarding an unequally-scaled steplength approach will often require fewer steps ...