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Application of Hamilton–Jacobi–Bellman Equation/Pontryagin’s Principle for Constrained Optimal Control
This article applies novel results for infinite- and finite-horizon optimal control problems with nonlinear dynamics and constraints. We use the...
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Fractional McKean–Vlasov and Hamilton–Jacobi–Bellman–Isaacs Equations
We study a class of abstract nonlinear fractional pseudo-differential equations in Banach spaces that includes both the McKean–Vlasov type equations...
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The large time profile for Hamilton–Jacobi–Bellman equations
Here, we study the large-time limit of viscosity solutions of the Cauchy problem for second-order Hamilton–Jacobi–Bellman equations with convex...
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Abstract McKean–Vlasov and Hamilton–Jacobi–Bellman Equations, Their Fractional Versions and Related Forward–Backward Systems on Riemannian Manifolds
AbstractWe introduce a class of abstract nonlinear fractional pseudo-differential equations in Banach spaces that includes both the McKean–Vlasov...
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The turnpike property and the longtime behavior of the Hamilton–Jacobi–Bellman equation for finite-dimensional LQ control problems
We analyze the consequences that the so-called turnpike property has on the longtime behavior of the value function corresponding to a...
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Optimal Controls of Stochastic Differential Equations with Jumps and Random Coefficients: Stochastic Hamilton–Jacobi–Bellman Equations with Jumps
We study the stochastic Hamilton–Jacobi–Bellman (HJB) equation with jump, which arises from a non-Markovian optimal control problem with a recursive...
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A semi-Lagrangian scheme for Hamilton–Jacobi–Bellman equations with oblique derivatives boundary conditions
We investigate in this work a fully-discrete semi-Lagrangian approximation of second order possibly degenerate Hamilton–Jacobi–Bellman (HJB)...
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Power-optimization of multistage non-isothermal chemical engine system via Onsager equations, Hamilton-Jacobi-Bellman theory and dynamic programming
The research on the output rate performance limit of the multi-stage energy conversion system based on modern optimal control theory is one of the...
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A comparison principle for semilinear Hamilton–Jacobi–Bellman equations in the Wasserstein space
The goal of this paper is to prove a comparison principle for viscosity solutions of semilinear Hamilton–Jacobi equations in the space of probability...
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Stochastic optimal control with random coefficients and associated stochastic Hamilton–Jacobi–Bellman equations
We consider the optimal control problem for stochastic differential equations (SDEs) with random coefficients under the recursive-type objective...
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Application of maximal monotone operator method for solving Hamilton–Jacobi–Bellman equation arising from optimal portfolio selection problem
In this paper, we investigate a fully nonlinear evolutionary Hamilton–Jacobi–Bellman (HJB) parabolic equation utilizing the monotone operator...
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Mixed Use of Pontryagin’s Principle and the Hamilton-Jacobi-Bellman Equation in Infinite- and Finite-Horizon Constrained Optimal Control
This paper proposes a framework for solving a class of nonlinear infinite- and finite-horizon optimal control problems with constraints....
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Minimax and Viscosity Solutions of Hamilton–Jacobi–Bellman Equations for Time-Delay Systems
The paper deals with a Bolza optimal control problem for a dynamical system, whose motion is described by a delay differential equation under an...
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Representation of Weak Solutions of Convex Hamilton–Jacobi–Bellman Equations on Infinite Horizon
In the present paper, it is provided a representation result for the weak solutions of a class of evolutionary Hamilton–Jacobi–Bellman equations on...
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Stability and convergence of second order backward differentiation schemes for parabolic Hamilton–Jacobi–Bellman equations
We study a second order Backward Differentiation Formula (BDF) scheme for the numerical approximation of linear parabolic equations and nonlinear...
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Weak semiconvexity estimates for Schrödinger potentials and logarithmic Sobolev inequality for Schrödinger bridges
We investigate the quadratic Schrödinger bridge problem, a.k.a. Entropic Optimal Transport problem, and obtain weak semiconvexity and semiconcavity...
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Auxiliary Space Preconditioners for a \(C^{0}\) Finite Element Approximation of Hamilton–Jacobi–Bellman Equations with Cordes Coefficients
In the past decade, there are many works on the finite element methods for the fully nonlinear Hamilton–Jacobi–Bellman (HJB) equations with Cordes...
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Inequality assessment in a dynamic framework with heterogenous agents
We propose a method to carry out an inequality assessment in a dynamic and cross-sectional framework, by applying the dynamic version of a suitable...
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C0 finite element approximations of linear elliptic equations in non-divergence form and Hamilton–Jacobi–Bellman equations with Cordes coefficients
This paper is concerned with C 0 (non-Lagrange) finite element approximations of the linear elliptic equations in non-divergence form and the...
