In this paper we present a framework to generate tight convex relaxations for nonconvex generalized disjunctive programs. The proposed methodology builds on our recent work on bilinear and concave generalized disjunctive programs for which tight linear relaxations can be generated, and extends its application to nonlinear relaxations. This is particularly important for those cases in which the ...

We describe a new temporal verification framework for safety and robustness analysis of nonlinear control laws, our target application being a space launcher vehicle. Robustness analysis, formulated as a nonconvex nonlinear optimization problem on admissible trajectories corresponding to piecewise polynomial dynamics, is relaxed into a convex linear programming problem on measures. This infinit...

This paper presents an algorithm for solving a class of large scale nonlinear programming problem which is originally derived from the multi-stage stochastic convex nonlinear programming. Using the Lagrangian-dual method and the Moreau-Yosida regularization, the primal problem is neatly transformed into a smooth convex problem. By introducing a self-concordant barrier function, an approximate g...

Process synthesis often involves the solution of large nonlinear discretecontinuous optimization problems, which are usually formulated as mixedinteger nonlinear programming (MINLP) or generalized disjunctive programming (GDP) problems and solved with MINLP solvers. This paper presents an efficient solution method for these problems named successive relaxed MINLP (SR-MINLP), where the model for...

This paper examines stability analysis of two classes of improved backward Euler methods, namely split-step $(theta, lambda)$-backward Euler (SSBE) and semi-implicit $(theta,lambda)$-Euler (SIE) methods, for nonlinear neutral stochastic delay differential equations (NSDDEs). It is proved that the SSBE method with $theta, lambdain(0,1]$ can recover the exponential mean-square stability with some...

In this paper, we introduce a General Logical Framework, called GLF, for defining Logical Frameworks, based on dependent types, in the style of the well known Edinburgh Logical Framework LF. The framework GLF features a generalized form of lambda abstraction where β-reductions fire provided the argument satisfies a logical predicate and may produce an n-ary substitution. The type system keeps t...