English
Related papers

Related papers: G\^ateaux semiderivative approach applied to shape…

200 papers

This paper focuses on optimization problems constrained by Parametric Variational Inequalities (PVI) defined on a moving set. Unlike most existing works on mathematical programs with equilibrium constraints, the equilibrium constraints have…

Optimization and Control · Mathematics 2026-03-06 Xiaojun Chen , Jin Zhang , Yixuan Zhang

We study an optimization problem that aims to determine the shape of an obstacle that is submerged in a fluid governed by the Stokes equations. The mentioned flow takes place in a channel, which motivated the imposition of a Poiseuille-like…

Numerical Analysis · Mathematics 2021-08-13 John Sebastian H. Simon , Hirofumi Notsu

We are interested in local quasi efficient solutions for nonsmooth vector optimization problems under new generalized approximate invexity assumptions. We formulate necessary and sufficient optimality conditions based on Stampacchia and…

Optimization and Control · Mathematics 2020-07-10 Mohsine Jennane , Lhoussain El Fadil , El Mostafa Kalmoun

This work is concerned with an optimal control problem governed by a non-smooth quasilinear elliptic equation with a nonlinear coefficient in the principal part that is locally Lipschitz continuous and directionally but not G\^ateaux…

Optimization and Control · Mathematics 2021-09-28 Christian Clason , Vu Huu Nhu , Arnd Rösch

We aim to solve a structured convex optimization problem, where a nonsmooth function is composed with a linear operator. When opting for full splitting schemes, usually, primal-dual type methods are employed as they are effective and also…

Optimization and Control · Mathematics 2019-05-17 Radu Ioan Bot , Axel Böhm

We consider a risk-averse optimal control problem governed by an elliptic variational inequality (VI) subject to random inputs. By deriving KKT-type optimality conditions for a penalised and smoothed problem and studying convergence of the…

Optimization and Control · Mathematics 2025-05-26 Amal Alphonse , Caroline Geiersbach , Michael Hintermüller , Thomas M. Surowiec

Shape optimization methods have been proven useful for identifying interfaces in models governed by partial differential equations. Here we consider a class of shape optimization problems constrained by nonlocal equations which involve…

Optimization and Control · Mathematics 2022-07-26 Volker Schulz , Matthias Schuster , Christian Vollmann

In this study, a shape optimization problem for the two-dimensional stationary Navier--Stokes equations with an artificial boundary condition is considered. The fluid is assumed to be flowing through a rectangular channel, and the…

Optimization and Control · Mathematics 2021-08-10 John Sebastian H. Simon , Hirofumi Notsu

This work proposes an implementable proximal-type method for a broad class of optimization problems involving nonsmooth and nonconvex objective and constraint functions. In contrast to existing methods that rely on an ad hoc model…

Optimization and Control · Mathematics 2024-09-26 Gregorio M. Sempere , Welington de Oliveira , Johannes O. Royset

In this work, we present new simple and optimal algorithms for solving the variational inequality (VI) problem for $p^{th}$-order smooth, monotone operators -- a problem that generalizes convex optimization and saddle-point problems. Recent…

Optimization and Control · Mathematics 2022-06-01 Deeksha Adil , Brian Bullins , Arun Jambulapati , Sushant Sachdeva

Variational analysis provides the theoretical foundations and practical tools for constructing optimization algorithms without being restricted to smooth or convex problems. We survey the central concepts in the context of a concrete but…

Optimization and Control · Mathematics 2025-04-08 Johannes O. Royset

We consider the shape optimization of an object in Navier--Stokes flow by employing a combined phase field and porous medium approach, along with additional perimeter regularization. By considering integral control and state constraints, we…

Optimization and Control · Mathematics 2018-12-04 Harald Garcke , Michael Hinze , Christian Kahle , Kei Fong Lam

Shape-constrained optimization arises in a wide range of problems including distributionally robust optimization (DRO) that has surging popularity in recent years. In the DRO literature, these problems are usually solved via reduction into…

Optimization and Control · Mathematics 2024-06-13 Henry Lam , Zhenyuan Liu , Dashi I. Singham

For a class of quasi-variational inequalities (QVIs) of obstacle-type the stability of its solution set and associated optimal control problems are considered. These optimal control problems are non-standard in the sense that they involve…

Optimization and Control · Mathematics 2020-08-25 Amal Alphonse , Michael Hintermüller , Carlos N. Rautenberg

In this paper, we investigate the nonemptiness of weak Pareto efficient solution set for a class of nonsmooth vector optimization problems on a nonempty closed constraint set without any boundedness and convexity assumptions. First, we…

Optimization and Control · Mathematics 2024-08-09 Danyang Liu , Jun Li , Giandomenico Mastroeni

Inclusion of contact in mechanical designs opens a large range of design possibilities, this includes classical designs with contact, such as gears, couplings, switches, clamps etc. However, incorporation of contact in topology optimization…

Computational Engineering, Finance, and Science · Computer Science 2023-05-12 Andreas Henrik Frederiksen , Ole Sigmund , Konstantinos Poulios

In this paper we propose a general algorithmic framework for first-order methods in optimization in a broad sense, including minimization problems, saddle-point problems and variational inequalities. This framework allows to obtain many…

Motivated by fatigue damage models, this paper addresses optimal control problems governed by a non-smooth system featuring two non-differentiable mappings. This consists of a coupling between a doubly non-smooth history-dependent evolution…

Optimization and Control · Mathematics 2023-02-14 Livia Betz

In this paper, we consider a dynamic viscoelastic contact problem with friction and wear, and describe it as a system of nonlinear partial differential equations. We formulate the previous problem as a hyperbolic quasi-variational…

Optimization and Control · Mathematics 2019-10-10 Tao Chen , Nan-jing Huang , Yi-bin Xiao

Variational inequalities, formulated on unknown dependent convex sets, are called quasi-variational inequalities (QVI). This paper is concerned with the abstract approach to a class of parabolic QVIs arising in many biochemical/mechanical…

Analysis of PDEs · Mathematics 2020-10-06 Maria Gokieli , Nobuyuki Kenmochi , Marek Niezgódka