Related papers: Accelerating design optimization using reduced ord…
The discretization of constrained nonlinear optimization problems arising in the field of topology optimization yields algebraic systems which are challenging to solve in practice, due to pathological ill-conditioning, strong nonlinearity…
We study the general approach to accelerating the convergence of the most widely used solution method of Markov decision processes with the total expected discounted reward. Inspired by the monotone behavior of the contraction mappings in…
Multi-material design optimization problems can, after discretization, be solved by the iterative solution of simpler sub-problems which approximate the original problem at an expansion point to first order. In particular, models…
We revisit gradient-based optimization for infinite projected entangled pair states (iPEPS), a tensor network ansatz for simulating many-body quantum systems. This approach is hindered by two major challenges: the high computational cost of…
For a time-limited version of the H$_2$ norm defined over a fixed time interval, we obtain a closed form expression of the gradients. After that, we use the gradients to propose a time-limited model order reduction method. The method…
Recent progress in deep learning has been driven by increasingly larger models. However, their computational and energy demands have grown proportionally, creating significant barriers to their deployment and to a wider adoption of deep…
Recent advances in convex optimization have leveraged computer-assisted proofs to develop optimized first-order methods that improve over classical algorithms. However, each optimized method is specially tailored for a particular problem…
We present a powerful general framework for designing data-dependent optimization algorithms, building upon and unifying recent techniques in adaptive regularization, optimistic gradient predictions, and problem-dependent randomization. We…
We deal with accelerating the solution of a sequence of large linear systems solved by preconditioned conjugate gradient method (PCG). The sequence originates from time-stepping within a simulation of an unsteady incompressible flow. We…
We present a globally convergent method to accelerate density-based topology optimization using projection-based reduced-order models (ROMs) and trust-region methods. To accelerate topology optimization, we replace the large-scale finite…
Reliability-based design optimization (RBDO) is traditionally formulated as a nested optimization and reliability problem. Although surrogate models are generally employed to improve efficiency, the approach remains computationally…
Dimensionality reduction is crucial for controlling nonlinear partial differential equations (PDE) through a "reduce-then-design" strategy, which identifies a reduced-order model and then implements model-based control solutions. However,…
Generative design refers to computational design methods that can automatically conduct design exploration under constraints defined by designers. Among many approaches, topology optimization-based generative designs aim to explore diverse…
First-order methods for solving convex optimization problems have been at the forefront of mathematical optimization in the last 20 years. The rapid development of this important class of algorithms is motivated by the success stories…
Process control and optimization have been widely used to solve decision-making problems in chemical engineering applications. However, identifying and tuning the best solution algorithm is challenging and time-consuming. Machine learning…
PDE-constrained optimization problems with control or state constraints are challenging from an analytical as well as numerical perspective. The combination of these constraints with a sparsity-promoting $\rm L^1$ term within the objective…
With the development of machine learning and Big Data, the concepts of linear and non-linear optimization techniques are becoming increasingly valuable for many quantitative disciplines. Problems of that nature are typically solved using…
In various scenarios, a single phase of modelling and solving is either not sufficient or not feasible to solve the problem at hand. A standard approach to solving AI planning problems, for example, is to incrementally extend the planning…
Nesterov's well-known scheme for accelerating gradient descent in convex optimization problems is adapted to accelerating stationary iterative solvers for linear systems. Compared with classical Krylov subspace acceleration methods, the…
The $\mathcal{H}_2$-optimal Model Order Reduction (MOR) is one of the most significant frameworks for reduction methodologies for linear dynamical systems. In this context, the Iterative Rational Krylov Algorithm (\IRKA) is a well…