A Time-Freezing Approach for Numerical Optimal Control of Nonsmooth Differential Equations With State Jumps

Numerical Analysis and Algorithms for Optimal Control of Partial Differential Equations with Control and State Constraints

An algorithm for efficient solution of control constrained optimal control problems is proposed and analyzed. It is based on an active set strategy involving primal as well as dual variables. For discretized problems sufficient conditions for convergence in finitely many iterations are given. Numerical examples are given and the role of strict complementarity condition is discussed.

Numerical methods for nonlinear stochastic differential equations with jumps

We present and analyse two implicit methods for Ito stochastic differential equations (SDEs) with Poisson-driven jumps. The first method, SSBE, is a split-step extension of the backward Euler method. The second method, CSSBE, arises from the introduction of a compensated, martingale, form of the Poisson process. We show that both methods are amenable to rigorous analysis when a one-sided Lipsch...

Numerical Analysis for Stochastic Partial Differential Delay Equations with Jumps

and Applied Analysis 3 (H3) There exists L 2 > 0 satisfying 󵄩󵄩󵄩h(x, y, u) 󵄩󵄩󵄩 2 H ≤ L 2 (‖x‖ 2 H + 󵄩󵄩󵄩y 󵄩󵄩󵄩 2 H ) , (12) for each x, y ∈ H and u ∈ Z. (H4) For ξ ∈ Db F0 0],H), there exists a constantL3 > 0 such that E ( 󵄨󵄨󵄨ξ (s) − ξ (t) 󵄨󵄨󵄨 2 ) ≤ L 3 |t − s| 2 , t, s ∈ [−τ, 0] . (13) We now describe our Euler-Maruyama scheme for the approximation of (1). For any n ≥ 1, let π n : H → H n = span{...

Numerical method for solving optimal control problem of the linear differential systems with inequality constraints

In this paper, an efficient method for solving optimal control problems of the linear differential systems with inequality constraint is proposed. By using new adjustment of hat basis functions and their operational matrices of integration, optimal control problem is reduced to an optimization problem. Also, the error analysis of the proposed method is nvestigated and it is proved that the orde...

Numerical Solution of Stochastic Differential Equations with Jumps in Finance