相关论文: Error estimates for a multiobjective optimal contr…

This paper tackles the multi-objective optimization of the cost functional of a path-following model predictive control for vehicle longitudinal and lateral control. While the inherent optimal character of the model predictive control and…

The imbalances and conditioning of the objective functions influence the performance of first-order methods for multiobjective optimization problems (MOPs). The latter is related to the metric selected in the direction-finding subproblems.…

The Bayesian inversion method demonstrates significant potential for solving inverse problems, enabling both point estimation and uncertainty quantification (UQ). However, Bayesian maximum a posteriori (MAP) estimation may become unstable…

Scalarization allows to solve a multi-objective optimization problem by solving many single-objective sub-problems, uniquely determined by some parameters. In this work, we propose several adaptive strategies to select such parameters in…

The numerical approximation of convection-dominated problems continues to remain subject of strong interest. Families of stabilization techniques for finite element methods were developed in the past. Adaptive techniques based on a…

In this chapter, we are concerned with inverse optimal control problems, i.e., optimization models which are used to identify parameters in optimal control problems from given measurements. Here, we focus on linear-quadratic optimal control…

We propose a novel numerical approach to compute the Pareto front in multivariate polynomial multi-objective optimization problems. When the objective functions and (equality) constraints are multivariate polynomials, the Pareto front,…

We describe algorithms, and experimental strategies, for the Pareto optimal control problem of simultaneously driving an arbitrary number of quantum observable expectation values to their respective extrema. Conventional quantum optimal…

In this paper, we propose a new descent method, termed as multiobjective memory gradient method, for finding Pareto critical points of a multiobjective optimization problem. The main thought in this method is to select a combination of the…

In this article a special class of nonlinear optimal control problems involving a bilinear term in the boundary condition is studied. These kind of problems arise for instance in the identification of an unknown space-dependent Robin…

In this work, we propose to efficiently solve time dependent parametrized optimal control problems governed by parabolic partial differential equations through the certified reduced basis method. In particular, we will exploit an error…

We investigate the application of a posteriori error estimates to a fractional optimal control problem with pointwise control constraints. Specifically, we address a problem in which the state equation is formulated as an integral form of…

This work reviews goal-oriented a posteriori error control, adaptivity and solver control for finite element approximations to boundary and initial-boundary value problems for stationary and non-stationary partial differential equations,…

We devise and analyze a reliable and efficient a posteriori error estimator for a semilinear control-constrained optimal control problem in two and three dimensional Lipschitz, but not necessarily convex, polytopal domains. We consider a…

In this paper we propose a linear scalarization proximal point algorithm for solving arbitrary lower semicontinuous quasiconvex multiobjective minimization problems. Under some natural assumptions and using the condition that the proximal…

We investigate the problem of computing a minimum set of solutions that approximates within a specified accuracy $\epsilon$ the Pareto curve of a multiobjective optimization problem. We show that for a broad class of bi-objective problems…

In this paper we propose a scalarization proximal point method to solve multiobjective unconstrained minimization problems with locally Lipschitz and quasiconvex vector functions. We prove, under natural assumptions, that the sequence…

Space-time finite element discretizations of time-optimal control problems governed by linear parabolic PDEs and subject to pointwise control constraints are considered. Optimal a priori error estimates are obtained for the control variable…

We deal with the numerical solution of linear partial differential equations (PDEs) with focus on the goal-oriented error estimates including algebraic errors arising by an inaccurate solution of the corresponding algebraic systems. The…

This work is concerned with optimal control problems where the objective functional consists of a tracking-type functional and an additional "multibang" regularization functional that promotes optimal control taking values from a given…