Related papers: A Contracted Path Integral Solution of the Discret…
This paper studies a class of non$-$Markovian singular stochastic control problems, for which we provide a novel probabilistic representation. The solution of such control problem is proved to identify with the solution of a $Z-$constrained…
In this work, solution of the finite horizon hybrid optimal control problem as the central element of the receding horizon optimal control (model predictive control) is investigated based on the indirect approach. The response of a hybrid…
This paper deals with the recoverable robust shortest path problem under the interval uncertainty representation. The problem is known to be strongly NP-hard and not approximable in general digraphs. Polynomial time algorithms for the…
We give a new proof of the trace formula for regular graphs. Our approach is inspired by path integral approach in quantum mechanics, and calculations are mostly combinatorial.
We develop an algorithmic theory of convex optimization over discrete sets. Using a combination of algebraic and geometric tools we are able to provide polynomial time algorithms for solving broad classes of convex combinatorial…
Discretizations of the Feynman-Kac path integral representation of the quantum mechanical density matrix are investigated. Each infinite-dimensional path integral is approximated by a Riemann integral over a finite-dimensional function…
The potential of the hybridized discontinuous Galerkin (HDG) method has been recognized for the computation of stationary flows. Extending the method to time-dependent problems can, e.g., be done by backward difference formulae (BDF) or…
Complex continuous or mixed joint distributions (e.g., P(Y | z_1, z_2, ..., z_N)) generally lack closed-form solutions, often necessitating approximations such as MCMC. This paper proposes Indeterminate Probability Theory (IPT), which makes…
This paper solves the dynamic portfolio choice problem. Using an explicit solution with a power utility, we construct a bridge between a continuous and discrete VAR model to assess portfolio sensitivities. We find, from a well analyzed…
The purpose of this paper is to introduce two new classes of accelerated distributed proximal conjugate gradient algorithms for multi-agent constrained optimization problems; given as minimization of a function decomposed as a sum of M…
The path integral formulation of constrained systems leads to obtain the equations of motion as total differential equations in many variables. If these equations are integrable then one can constuct a valid and a canonical phase space…
We consider a constrained version of the shortest path problem on the complete graphs whose edges have independent random lengths and costs. We establish the asymptotic value of the minimum length as a function of the cost-budget within a…
Time-fractional parabolic equations with a Caputo time derivative of order $\alpha\in(0,1)$ are discretised in time using collocation methods, which assume that the Caputo derivative of the computed solution is piecewise-polynomial. For…
We consider a general path-dependent version of the hedging problem with price impact of Bouchard et al. (2019), in which a dual formulation for the super-hedging price is obtained by means of PDE arguments, in a Markovian setting and under…
The optimal control of a mechanical system is of crucial importance in many realms. Typical examples are the determination of a time-minimal path in vehicle dynamics, a minimal energy trajectory in space mission design, or optimal motion…
This paper addresses the analysis and numerical assessment of a computational method for solving the Cahn--Hilliard equation defined on a surface. The proposed approach combines the stabilized trace finite element method for spatial…
The semiclassical approximation of the worldline path integral is a powerful tool to study nonperturbative electron-positron pair creation in spacetime-dependent background fields. Finding solutions of the classical equations of motion,…
In this paper we present the first deterministic polynomial time algorithm for determining the existence of a Hamiltonian cycle and finding a Hamiltonian cycle in general graphs. Our algorithm can also solve the Hamiltonian path problem in…
This paper investigates a numerical probabilistic method for the solution of some semilinear stochastic partial differential equations (SPDEs in short). The numerical scheme is based on discrete time approximation for solutions of systems…
A c-number path integral representation is constructed for the solution of the Dirac equation. The integration is over the real trajectories in the continuous three-space and other two canonical pairs of compact variables controlling the…