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This paper presents an efficient gradient projection-based method for structural topological optimization problems characterized by a nonlinear objective function which is minimized over a feasible region defined by bilateral bounds and a…
We suggest simple implementable modifications of conditional gradient and gradient projection methods for smooth convex optimization problems in Hilbert spaces. Usually, the custom methods attain only weak convergence. We prove strong…
To facilitate widespread adoption of automated engineering design techniques, existing methods must become more efficient and generalizable. In the field of topology optimization, this requires the coupling of modern optimization methods…
In this work, we consider a class of convex optimization problems in a real Hilbert space that can be solved by performing a single projection, i.e., by projecting an infeasible point onto the feasible set. Our results improve those…
This paper investigates simple bilevel optimization problems where we minimize an upper-level objective over the optimal solution set of a convex lower-level objective. Existing methods for such problems either only guarantee asymptotic…
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…
This paper is concerned with topology optimization based on a level set method using (doubly) nonlinear diffusion equations. Topology optimization using the level set method is called level set-based topology optimization, which is possible…
We present a new method for stochastic shape optimisation of engineering structures. The method generalises an existing deterministic scheme, in which the structure is represented and evolved by a level-set method coupled with mathematical…
This paper presents an adaptive discretization strategy for level set topology optimization of structures based on hierarchical B-splines. This work focuses on the influence of the discretization approach and the adaptation strategy on the…
We exploit level set topology optimization to find the optimal material distribution for metamaterial-based heat manipulators. The level set function, geometry, and solution field are parameterized using the non-uniform rational B-spline…
This paper presents a novel computational scheme for sensitivity analysis of the velocity field in the level set method using the discrete adjoint method. The velocity field is represented in B-spline space, and the adjoint equations are…
Many clustering applications in machine learning and data mining rely on solving metric-constrained optimization problems. These problems are characterized by $O(n^3)$ constraints that enforce triangle inequalities on distance variables…
Many applications in vision require estimation of thin structures such as boundary edges, surfaces, roads, blood vessels, neurons, etc. Unlike most previous approaches, we simultaneously detect and delineate thin structures with sub-pixel…
Suppose that there is a ground set which consists of a large number of vectors in a Hilbert space. Consider the problem of selecting a subset of the ground set such that the projection of a vector of interest onto the subspace spanned by…
This paper provides an extended level set (X-LS) based topology optimiza- tion method for multi material design. In the proposed method, each zero level set of a level set function {\phi}ij represents the boundary between materials i and j.…
Bilevel optimization is an important class of optimization problems where one optimization problem is nested within another. While various methods have emerged to address unconstrained general bilevel optimization problems, there has been a…
A surrogate-based topology optimisation algorithm for linear elastic structures under parametric loads and boundary conditions is proposed. Instead of learning the parametric solution of the state (and adjoint) problems or the optimisation…
This paper considers a networked system with a finite number of users and supposes that each user tries to minimize its own private objective function over its own private constraint set. It is assumed that each user's constraint set can be…
Optimization, a key tool in machine learning and statistics, relies on regularization to reduce overfitting. Traditional regularization methods control a norm of the solution to ensure its smoothness. Recently, topological methods have…
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…