Related papers: Efficient algorithm for linear diophantine equatio…
We study a deflation method to reduce and to solve linear dfferential-algebraic equations (DAEs). It consists to define a sequence of DAEs with index reduction of one unit by step. This is simultaneously performed by substitution and…
High quality AI solutions require joint optimization of AI algorithms and their hardware implementations. In this work, we are the first to propose a fully simultaneous, efficient differentiable DNN architecture and implementation co-search…
Distributed Constraint Optimization Problems (DCOPs) have been widely used to coordinate interactions (i.e. constraints) in cooperative multi-agent systems. The traditional DCOP model assumes that variables owned by the agents can take only…
Extended Affine (EA) equivalence is the equivalence relation between two vectorial Boolean functions $F$ and $G$ such that there exist two affine permutations $A$, $B$, and an affine function $C$ satisfying $G = A \circ F \circ B + C$.…
This letter presents a method to reduce the computational demands of including second-order dynamics sensitivity information into the Differential Dynamic Programming (DDP) trajectory optimization algorithm. An approach to DDP is developed…
We obtain an essentially optimal estimate for the moment of order 32/3 of the exponential sum having argument $\alpha x^3+\beta x^2$. Subject to modest local solubility hypotheses, we thereby establish that pairs of diagonal Diophantine…
Neural ordinary differential equations (Neural ODEs) propose the idea that a sequence of layers in a neural network is just a discretisation of an ODE, and thus can instead be directly modelled by a parameterised ODE. This idea has had…
We present an algorithm for the rigorous integration of Delay Differential Equations (DDEs) of the form $x'(t)=f(x(t-\tau),x(t))$. As an application, we give a computer assisted proof of the existence of two attracting periodic orbits…
Fast Fourier transform algorithms are an arsenal of effective tools for solving various problems of analysis and high-speed processing of signals of various natures. Almost all of these algorithms are designed to process sequences of…
We present the Deep Picard Iteration (DPI) method, a new deep learning approach for solving high-dimensional partial differential equations (PDEs). The core innovation of DPI lies in its use of Picard iteration to reformulate the typically…
Since the beginning of the development of interior-point methods, there exists a puzzling gap between the results in theory and the observations in numerical experience, i.e., algorithms with good polynomial bound are not computationally…
This paper proposes an efficient algorithm for solving the Hartree--Fock equation combining a multilevel correction scheme with an adaptive refinement technique to improve computational efficiency. The algorithm integrates a multilevel…
In this paper we present the solver DuQuad specialized for solving general convex quadratic problems arising in many engineering applications. When it is difficult to project on the primal feasible set, we use the (augmented) Lagrangian…
The time parallel solution of optimality systems arising in PDE constraint optimization could be achieved by simply applying any time parallel algorithm, such as Parareal, to solve the forward and backward evolution problems arising in the…
In robust optimization problems, the magnitude of perturbations is relatively small. Consequently, solutions within certain regions are less likely to represent the robust optima when perturbations are introduced. Hence, a more efficient…
We propose machine learning methods for solving fully nonlinear partial differential equations (PDEs) with convex Hamiltonian. Our algorithms are conducted in two steps. First the PDE is rewritten in its dual stochastic control…
In this paper we synthesize behavioral ideas with geometric control theory and propose a unified geometric framework for representing all solutions of a Linear Time Invariant Differential-Algebraic Equation (DAE-LTI) as outputs of classical…
In this paper we consider a method of solving optimal stopping problems in discrete and continuous time based on their dual representation. A novel and generic simulation-based optimization algorithm not involving nested simulations is…
Differential evolution (DE) is an effective global evolutionary optimization algorithm using to solve global optimization problems mainly in a continuous domain. In this field, researchers pay more attention to improving the capability of…
The asymptotic iteration method (AIM) is an iterative technique used to find exact and approximate solutions to second-order linear differential equations. In this work, we employed AIM to solve systems of two first-order linear…