Related papers: A new alternating direction trust region method ba…
This work investigates the theoretical performance of the alternating-direction method of multipliers (ADMM) as it applies to nonconvex optimization problems, and in particular, problems with nonconvex constraint sets. The alternating…
We consider trust-region methods for solving optimization problems where the objective is the sum of a smooth, nonconvex function and a nonsmooth, convex regularizer. We extend the global convergence theory of such methods to include…
This paper introduces new perspectives on analog design space search. To minimize the time-to-market, this endeavor better cast as constraint satisfaction problem than global optimization defined in prior arts. We incorporate model-based…
Solving parabolic optimal control problems can be inherently challenging in the field of science and engineering, especially with constraints on the nonsmooth distributed control. Motivated by the extensive applicability of the alternating…
Constrained optimization in high-dimensional black-box settings is difficult due to expensive evaluations, the lack of gradient information, and complex feasibility regions. In this work, we propose a Bayesian optimization method that…
Constrained non-convex optimization problems frequently arise in control applications. Solving such problems is inherently challenging, as existing methods often converge to suboptimal local minima or incur prohibitive computational costs.…
In this contribution we device and analyze improved variants of the non-conforming dual approach for trust-region reduced basis (TR-RB) approximation of PDE-constrained parameter optimization that has recently been introduced in [Keil et…
In this paper (part 1), we describe a derivative-free trust-region method for solving unconstrained optimization problems. We will discuss a method when we relax the model order assumption and use artificial neural network techniques to…
This paper addresses the compliance minimization of a truss, where the number of available nodes is limited. It is shown that this optimization problem can be recast as a second-order cone programming with a cardinality constraint. We…
Alternating direction multiplication is a powerful technique for solving convex optimisation problems. When challenging subproblems are encountered in the real world, it is useful to solve them by introducing neighbourhood terms. When the…
We introduce two multifidelity trust-region methods based on the Magical Trust Region (MTR) framework. MTR augments the classical trust-region step with a secondary, informative direction. In our approaches, the secondary ``magical''…
In this paper, we introduce a graph matching method that can account for constraints of arbitrary order, with arbitrary potential functions. Unlike previous decomposition approaches that rely on the graph structures, we introduce a…
The trust region subproblem (TRS) is to minimize a possibly nonconvex quadratic function over a Euclidean ball. There are typically two cases for (TRS), the so-called ``easy case'' and ``hard case''. Even in the ``easy case'', the sequence…
Physics-informed machine learning and inverse modeling require the solution of ill-conditioned non-convex optimization problems. First-order methods, such as SGD and ADAM, and quasi-Newton methods, such as BFGS and L-BFGS, have been applied…
In this article, we develop a trust-region technique to find critical points of unconstrained set optimization problems with the objective set-valued map defined by finitely many twice continuously differentiable functions. The technique is…
This paper considers an explicit continuation method and the trust-region updating strategy for the unconstrained optimization problem. Moreover, in order to improve its computational efficiency and robustness, the new method uses the…
Two-trust-region subproblem (TTRS), which is the minimization of a general quadratic function over the intersection of two full-dimensional ellipsoids, has been the subject of several recent research. In this paper, to solve TTRS, a hybrid…
We consider unconstrained multi-criteria optimization problems with finite sum objective functions. The proposed algorithm belongs to a non-monotone trust region framework where additional sampling approach is used to govern the sample size…
Inexact alternating direction multiplier methods (ADMMs) are developed for solving general separable convex optimization problems with a linear constraint and with an objective that is the sum of smooth and nonsmooth terms. The approach…
Most of the optimal guidance problems can be formulated as nonconvex optimization problems, which can be solved indirectly by relaxation, convexification, or linearization. Although these methods are guaranteed to converge to the global…