相关论文: A simplified derivation technique of topological d…

In this paper we present a methodology that allows the efficient computation of the topological derivative for semilinear elliptic problems within the averaged adjoint Lagrangian framework. The generality of our approach should also allow…

While topological derivatives have proven useful in applications of topology optimisation and inverse problems, their mathematically rigorous derivation remains an ongoing research topic, in particular in the context of nonlinear partial…

The objective of this paper is to introduce and demonstrate a robust method for multi-constrained topology optimization. The method is derived by combining the topological sensitivity with the classic augmented Lagrangian formulation. The…

The topological derivative represents the sensitivity of a domain-dependent functional with respect to a local perturbation of the domain and is a valuable tool in topology optimization. Motivated by an application from electrical…

In this paper we develop a method to solve evolution equations on Gelfand triples with time-fractional derivative based on monotonicity techniques. Applications include deterministic and stochastic quasi-linear partial differential…

We consider optimal control problems, where the control appears in the main part of the operator. We derive the Pontryagin maximum principle as a necessary optimality condition. The proof uses the concept of topological derivatives. In…

In this paper we introduce the topological state derivative for general topological dilatations and explore its relation to standard optimal control theory. We show that for a class of partial differential equations, the shape dependent…

Hidden convexity is a powerful idea in optimization: under the right transformations, nonconvex problems that are seemingly intractable can be solved efficiently using convex optimization. We introduce the notion of a Lagrangian dual…

In this paper, we perform a rigourous version of shape and topological derivatives for optimizations problems under constraint Helmoltz problems. A shape and topological optimization problem is formulated by introducing cost functional. We…

In this paper we examine how Lagrangian techniques can be used to compute underapproximations and overapproximation of the finite-time horizon, stochastic reach-avoid level sets for discrete-time, nonlinear systems. This approach is…

We study quasi-convex optimization problems, where only a subset of the constraints can be sampled, and yet one would like a probabilistic guarantee on the obtained solution with respect to the initial (unknown) optimization problem. Even…

This paper is devoted to the theoretical and numerical investigation of an augmented Lagrangian method for the solution of optimization problems with geometric constraints. Specifically, we study situations where parts of the constraints…

In this paper, a projected primal-dual gradient flow of augmented Lagrangian is presented to solve convex optimization problems that are not necessarily strictly convex. The optimization variables are restricted by a convex set with…

Foundations of a new projection-based model reduction approach for convection dominated nonlinear fluid flows are summarized. In this method the evolution of the flow is approximated in the Lagrangian frame of reference. Global basis…

In this paper we study an abstract framework for computing shape derivatives of functionals subject to PDE constraints. We revisit the Lagrangian approach using the implicit function theorem in an abstract setting tailored for applications…

In this paper we investigate how standard nonlinear programming algorithms can be used to solve constrained optimization problems in a distributed manner. The optimization setup consists of a set of agents interacting through a…

Many non-iterative imaging algorithms require a large number of incident directions. Topological derivative-based imaging techniques can alleviate this problem, but lacks a theoretical background and a definite means of selecting the…

Semi-Lagrangian methods have traditionally been developed in the framework of hyperbolic equations, but several extensions of the Semi-Lagrangian approach to diffusion and advection--diffusion problems have been proposed recently. These…

We propose and analyze a numerical method to solve an elliptic transmission problem in full space. The method consists of a variational formulation involving standard boundary integral operators on the coupling interface and an ultra-weak…

This paper proposes a novel distributed semismooth Newton based augmented Lagrangian method for solving a class of optimization problems over networks, where the global objective is defined as the sum of locally held cost functions, and…