Related papers: A duality principle and related computational meth…
This paper presents a canonical duality approach for solving a general topology optimization problem of nonlinear elastic structures. By using finite element method, this most challenging problem can be formulated as a mixed integer…
This article develops a duality principle for non-linear elasticity. The results are obtained through standard tools of convex analysis and the Legendre transform concept. We emphasize the dual variational formulation is concave. Moreover,…
In this article we develop a duality principle suitable for a large class of problems in optimization. The main result is obtained through basic tools of convex analysis and duality theory. We establish a correct relation between the…
In the current industry, the development of optimized mechanical components able to satisfy the customer requirements evolves quickly. Therefore, companies are asked for efficient solutions to improve their products in terms of stiffness…
A common problem in the optimization of structures is the handling of uncertainties in the parameters. If the parameters appear in the constraints, the uncertainties can lead to an infinite number of constraints. Usually the constraints…
In this article, we develop duality principles applicable to primal variational formulations found in the non-linear elasticity theory. As a first application, we establish the concerning results in details for one and three-dimensional…
This article develops a duality principle for a class of optimization problems in $\mathbb{R}^n$. The results are obtained based on standard tools of convex analysis and on a well known result of Toland for D.C. optimization. Global…
Topology optimization has matured to become a powerful engineering design tool that is capable of designing extraordinary structures and materials taking into account various physical phenomena. Despite the method's great advancements in…
In this paper we consider a distributed optimization scenario in which a set of agents has to solve a convex optimization problem with separable cost function, local constraint sets and a coupling inequality constraint. We propose a novel…
Topology optimization problems often support multiple local minima due to a lack of convexity. Typically, gradient-based techniques combined with continuation in model parameters are used to promote convergence to more optimal solutions;…
The task of finding the smallest energy needed to bring a solid to its onset of mechanical instability arises in many problems in materials science, from the determination of the elasticity limit to the consistent assignment of free…
Bilevel optimization problems embed the optimality of a subproblem as a constraint of another optimization problem. We introduce the concept of near-optimality robustness for bilevel optimization, protecting the upper-level solution…
Designing high-performance electric machines that maintain their efficiency and reliability under uncertain material and operating conditions is crucial for industrial applications. In this paper, we present a novel framework for robust…
We propose a new algorithm for the solution of the robust multiple-load topology optimization problem. The algorithm can be applied to any type of problem, e.g., truss topology, variable thickness sheet or free material optimization. We…
The paper presents a new method for shape and topology optimization based on an efficient and scalable boundary integral formulation for elasticity. To optimize topology, our approach uses iterative extraction of isosurfaces of a…
This article develops duality principles applicable to the non-linear Kirchhoff-Love model of plates. The results are obtained through standard tools of convex analysis, functional analysis, calculus of variations and duality theory. The…
This article studies problems of optimal transport, by embedding them in a general functional analytic framework of convex optimization. This provides a unified treatment of a large class of related problems in probability theory and allows…
This paper presents tractable reformulations of topology optimization problems of structures subject to frictionless unilateral contact conditions. Specifically, we consider stiffness maximization problems of trusses and continua. Based on…
This article aims to introduce the paradigm of distributional robustness from the field of convex optimization to tackle optimal design problems under uncertainty. We consider realistic situations where the physical model, and thereby the…
Robust and distributionally robust optimization are modeling paradigms for decision-making under uncertainty where the uncertain parameters are only known to reside in an uncertainty set or are governed by any probability distribution from…