In this paper we consider infinite dimensional linear programming problems and study its connections with nonlinear partial differential equations.

Using a known algebraic result, we obtain finite polynomial programming reformulation of semi-infinite program modeling the aircraft deconfliction problem via subliminal speed regulation. Solving yields better results than state art for most tested instances.

A portfolio optimization problem on an infinite time horizon is considered. Risky asset price obeys a logarithmic Brownian motion, and the interest rate varies according to an ergodic Markov diffusion process. Moreover, the interest rate fluctuation is correlated with the risky asset price fluctuation. The goal is to choose optimal investment and consumption policies to maximize the infinite ho...

We develop an iterative method for solving the KKT system of the semi-infinite programming (SIP) problem. At each iteration, we solve the KKT system of a nonlinear programming problem with finite constraints by a semismooth Newton method. The algorithm either terminates at a KKT point of the SIP problem in finitely many iterations or generates an infinite sequence of iterates whose any accumula...

Domain theory is ‘a mathematical theory that serves as a foundation for the semantics of programming languages’ [AJ94]. Domains form the basis of a theory of partial information, which extends the familiar notion of partial function to encompass a whole spectrum of “degrees of definedness”, so as to model incremental higher-order computation (i.e., computing with infinite data values, such as f...

In a common formulation of semi-infinite programs, the infinite constraint set is a requirement that a function parametrized by the decision variables is nonnegative over an interval. If this function is sufficiently closely approximable by a polynomial or a rational function, then the semi-infinite program can be reformulated as an equivalent semidefinite program. Solving this semidefinite pro...

We integrate ontology languages and logic programming (LP) by extending disjunctive logic programs (DLPs) and their semantics in order to support inverses and an infinite universe, without introducing function symbols. We show that this extension is still decidable, and can be used to simulate, on the one hand, answer set programming with a finite universe, and on the other hand, several expres...

Logic Programming is a Turing complete language. As a consequence, designing algorithms that decide termination and non-termination of programs or decide inductive/coinductive soundness of formulae is a challenging task. For example, the existing state-of-the-art algorithms can only semi-decide coinductive soundness of queries in logic programming for regular formulae. Another, less famous, but...

In this paper, we calculated 37 structural descriptors of 174 organic compounds. The 154 molecules were used to derive quantitative structure – infinite dilution activity coefficient relationship by genetic programming, the other 20 compounds were used to test the model. The result showed that molecular partition property and three-dimensional structural descriptors have significant influence o...