Related papers: A Subspace Minimization Barzilai-Borwein Method fo…
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 consider a generic min-max multi-objective bilevel optimization problem with applications in robust machine learning such as representation learning and hyperparameter optimization. We design MORBiT, a novel single-loop gradient…
Many real-world multi-objective optimisation problems rely on computationally expensive function evaluations. Multi-objective Bayesian optimisation (BO) can be used to alleviate the computation time to find an approximated set of Pareto…
For a wide range of applications the structure of systems like Neural Networks or complex simulations, is unknown and approximation is costly or even impossible. Black-box optimization seeks to find optimal (hyper-) parameters for these…
For optimization problems on Riemannian manifolds, many types of globally convergent algorithms have been proposed, and they are often equipped with the Riemannian version of the Armijo line search for global convergence. Such existing…
We consider the composite minimization problem with the objective function being the sum of a continuously differentiable and a merely lower semicontinuous and extended-valued function. The proximal gradient method is probably the most…
Zeroth-order (ZO) optimization has emerged as a promising alternative to gradient-based backpropagation methods, particularly for black-box optimization and large language model (LLM) fine-tuning. However, ZO methods often suffer from slow…
The Barzilai and Borwein (BB) gradient method is one of the most widely-used line-search gradient methods. It computes the step-size for the current iterate by using the information carried in the previous iteration. Recently, William Kahan…
This paper deals with the problem of multi-degree reduction of a composite B\'ezier curve with the parametric continuity constraints at the endpoints of the segments. We present a novel method which is based on the idea of using constrained…
In this work we propose MirrorCBO, a consensus-based optimization (CBO) method which generalizes standard CBO in the same way that mirror descent generalizes gradient descent. For this we apply the CBO methodology to a swarm of dual…
We analyze a pointwise tracking multiobjective optimal control problem subject to the Poisson problem and bilateral control constraints. To approximate Pareto optimal points and the Pareto front numerically, we consider two different finite…
Real-world problems often involve the optimization of several objectives under multiple constraints. An example is the hyper-parameter tuning problem of machine learning algorithms. In particular, the minimization of the estimation of the…
Optimizing expensive-to-evaluate black-box functions of discrete (and potentially continuous) design parameters is a ubiquitous problem in scientific and engineering applications. Bayesian optimization (BO) is a popular, sample-efficient…
The low-rank stochastic semidefinite optimization has attracted rising attention due to its wide range of applications. The nonconvex reformulation based on the low-rank factorization, significantly improves the computational efficiency but…
The limited memory steepest descent method (LMSD) proposed by Fletcher is an extension of the Barzilai-Borwein "two-point step size" strategy for steepest descent methods for solving unconstrained optimization problems. It is known that the…
Optimal damping aims at determining a vector of damping coefficients $\nu$ that maximizes the decay rate of a mechanical system's response. This problem can be formulated as the minimization of the trace of the solution of a Lyapunov…
This paper considers the simple bilevel optimization (SBO) problem, which minimizes a composite convex function over the optimal solution set of another composite convex minimization problem. We first show that this bilevel problem is…
Majorization-minimization algorithms consist of successively minimizing a sequence of upper bounds of the objective function so that along the iterations the objective function decreases. Such a simple principle allows to solve a large…
In recent years, there has been significant research interest in solving Quadratic Unconstrained Binary Optimisation (QUBO) problems. Physics-inspired optimisation algorithms have been proposed for deriving optimal or sub-optimal solutions…
Bayesian optimization (BO) is a popular global optimization scheme for sample-efficient optimization in domains with expensive function evaluations. The existing BO techniques are capable of finding a single global optimum solution.…