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In graph signal processing, learning the weighted connections between nodes from a set of sample signals is a fundamental task when the underlying relationships are not known a priori. This task is typically addressed by finding a graph…

In this paper, the stabilized finite element method based on local projection is applied to discretize the Stokes eigenvalue problems and the corresponding convergence analysis is given. Furthermore, we also use a method to improve the…

Prediction+optimization is a common real-world paradigm where we have to predict problem parameters before solving the optimization problem. However, the criteria by which the prediction model is trained are often inconsistent with the goal…

Decentralized optimization is a powerful paradigm that finds applications in engineering and learning design. This work studies decentralized composite optimization problems with non-smooth regularization terms. Most existing gradient-based…

In this paper, we propose a multilevel stochastic framework for the solution of nonconvex unconstrained optimization problems. The proposed approach uses random regularized first-order models that exploit an available hierarchical…

This paper presents a computational framework for the robust stiffness design of hyperelastic structures at finite deformations subject to various uncertain sources. In particular, the loading, material properties, and geometry…

This work is devoted to the development and analysis of a linearization algorithm for microscopic elliptic equations, with scaled degenerate production, posed in a perforated medium and constrained by the homogeneous Neumann-Dirichlet…

This paper proposes topology optimization for considering shielding and penetrating features. Based on the fictitious physical model, which is a useful approach to control geometric features, the proposed method analyzes fictitious…

We propose a novel level set-based topology optimization for micropolar solids subjected to thermo-mechanical loading. To capture the size effects, we have incorporated the microstructural length-scale information into the level set-based…

We propose a regularized saddle-point algorithm for convex networked optimization problems with resource allocation constraints. Standard distributed gradient methods suffer from slow convergence and require excessive communication when…

We present a level-set based topology optimization algorithm for design optimization problems involving an arbitrary number of different materials, where the evolution of a design is solely guided by topological derivatives. Our method can…

We develop a computationally efficient algorithm for the automatic regularization of nonlinear inverse problems based on the discrepancy principle. We formulate the problem as an equality constrained optimization problem, where the…

Gradient porous structured materials possess significant potential of being applied in many engineering fields. To accelerate the design process of infill graded microstructures, a novel asymptotic homogenisation topology optimisation…

We present a new feasible proximal gradient method for constrained optimization where both the objective and constraint functions are given by the summation of a smooth, possibly nonconvex function and a convex simple function. The…

This paper is devoted to the class of paraconvex functions and presents some of its fundamental properties, characterization, and examples that can be used for their recognition and optimization. Next, the convergence analysis of the…

Constrained bilevel optimization tackles nested structures present in constrained learning tasks like constrained meta-learning, adversarial learning, and distributed bilevel optimization. However, existing bilevel optimization methods…

We present a rigorous convergence analysis of a new method for density-based topology optimization that provides point-wise bound preserving design updates and faster convergence than other popular first-order topology optimization methods.…

In this paper, we propose a high-order extension of the multiscale method introduced by the authors in [SIAM J. Numer. Anal., 63(4) (2025), pp. 1617--1641] for heterogeneous Stokes problems, while also providing several other improvements,…

A new approach for generating stress-constrained topological designs in continua is presented. The main novelty is in the use of elasto-plastic modeling and in optimizing the design such that it will exhibit a linear-elastic response. This…

We develop a novel theoretical framework for understating OT schemes respecting a class structure. For this purpose, we propose a convex OT program with a sum-of-norms regularization term, which provably recovers the underlying class…