Related papers: A derivative-free method for structured optimizati…
The aim of structured optimization is to assemble a solution, using a given set of (possibly uncountably infinite) atoms, to fit a model to data. A two-stage algorithm based on gauge duality and bundle method is proposed. The first stage…
An algorithm based on the interior-point methodology for solving continuous nonlinearly constrained optimization problems is proposed, analyzed, and tested. The distinguishing feature of the algorithm is that it presumes that only noisy…
Approximations of functions with finite data often do not respect certain "structural" properties of the functions. For example, if a given function is non-negative, a polynomial approximation of the function is not necessarily also…
In this paper, we propose and analyze zeroth-order stochastic approximation algorithms for nonconvex and convex optimization, with a focus on addressing constrained optimization, high-dimensional setting and saddle-point avoiding. To handle…
Many high-dimensional optimisation problems exhibit rich geometric structures in their set of minimisers, often forming smooth manifolds due to over-parametrisation or symmetries. When this structure is known, at least locally, it can be…
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…
Fast, gradient-based structural optimization has long been limited to a highly restricted subset of problems -- namely, density-based compliance minimization -- for which gradients can be analytically derived. For other objective functions,…
In this paper, we propose an exact general algorithm for solving non-convex optimization problems, where the non-convexity arises due to the presence of an inverse S-shaped function. The proposed method involves iteratively approximating…
We present a stochastic descent algorithm for unconstrained optimization that is particularly efficient when the objective function is slow to evaluate and gradients are not easily obtained, as in some PDE-constrained optimization and…
In this article we consider shape optimization problems as optimal control problems via the method of mappings. Instead of optimizing over a set of admissible shapes a reference domain is introduced and it is optimized over a set of…
An interior-point algorithm framework is proposed, analyzed, and tested for solving nonlinearly constrained continuous optimization problems. The main setting of interest is when the objective and constraint functions may be nonlinear…
In this paper, we propose a new Fully Composite Formulation of convex optimization problems. It includes, as a particular case, the problems with functional constraints, max-type minimization problems, and problems of Composite…
When gradient-based methods are impractical, black-box optimization (BBO) provides a valuable alternative. However, BBO often struggles with high-dimensional problems and limited trial budgets. In this work, we propose a novel approach…
This paper considers a class of convex optimization problems where both, the objective function and the constraints, have a continuously varying dependence on time. Our goal is to develop an algorithm to track the optimal solution as it…
This paper analyzes the performance of the Fractal Decomposition Algorithm (FDA) metaheuristic applied to low-dimensional continuous optimization problems. This algorithm was originally developed specifically to deal efficiently with…
We present a numerical method to efficiently solve optimization problems governed by large-scale nonlinear systems of equations, including discretized partial differential equations, using projection-based reduced-order models accelerated…
In derivative-free and blackbox optimization, the objective function is often evaluated through the execution of a computer program seen as a blackbox. It can be noisy, in the sense that its outputs are contaminated by random errors.…
Combinatorial optimization can be described as the problem of finding a feasible subset that maximizes a objective function. The paper discusses combinatorial optimization problems, where for each dimension the set of feasible subsets is…
Black box discrete optimization (BBDO) appears in wide range of engineering tasks. Evolutionary or other BBDO approaches have been applied, aiming at automating necessary tuning of system parameters, such as hyper parameter tuning of…
Benchmarking is essential for developing and evaluating black-box optimization algorithms, providing a structured means to analyze their search behavior. Its effectiveness relies on carefully selected problem sets used for evaluation. To…