Related papers: Geometry on Optimal Problem
The paper considers the minimization of a separable convex function subject to linear ascending constraints. The problem arises as the core optimization in several resource allocation scenarios, and is a special case of an optimization of a…
We present a general technique, based on parametric search with some twist, for solving a variety of optimization problems on a set of semi-algebraic geometric objects of constant complexity. The common feature of these problems is that…
We consider the problem of embedding the nodes of a hypergraph into Euclidean space under the assumption that the interactions arose through closeness to unknown hyperedge centres. In this way, we tackle the inverse problem associated with…
In typical applications of Bayesian optimization, minimal assumptions are made about the objective function being optimized. This is true even when researchers have prior information about the shape of the function with respect to one or…
This paper proposes novel algorithm for non-convex multimodal constrained optimisation problems. It is based on sequential solving restrictions of problem to sections of feasible set by random subspaces (in general, manifolds) of low…
Bayesian optimization is normally performed within fixed variable bounds. In cases like hyperparameter tuning for machine learning algorithms, setting the variable bounds is not trivial. It is hard to guarantee that any fixed bounds will…
The Expectation--Maximization (EM) algorithm is a simple meta-algorithm that has been used for many years as a methodology for statistical inference when there are missing measurements in the observed data or when the data is composed of…
We present a geometric multilevel optimization approach that smoothly incorporates box constraints. Given a box constrained optimization problem, we consider a hierarchy of models with varying discretization levels. Finer models are…
Prune-and-search is an important paradigm for solving many important geometric problems. We show that the general prune-and-search technique can be implemented where the objects are given in read-only memory. As examples we consider…
Information Geometry has been used to inspire efficient algorithms for stochastic optimization, both in the combinatorial and the continuous case. We give an overview of the authors' research program and some specific contributions to the…
Nonconvexity induced by the nonlinear AC power flow equations challenges solution algorithms for AC optimal power flow (OPF) problems. While significant research efforts have focused on reliably computing high-quality OPF solutions, it is…
What is the effectiveness of local search algorithms for geometric problems in the plane? We prove that local search with neighborhoods of magnitude $1/\epsilon^c$ is an approximation scheme for the following problems in the Euclidian…
This paper introduces a graph-based, potential-guided method for path planning problems in unknown environments, where obstacles are unknown until the robots are in close proximity to the obstacle locations. Inspired by optimal transport…
Geometric modeling by constraints, whose applications are of interest to communities from various fields such as mechanical engineering, computer aided design, symbolic computation or molecular chemistry, is now integrated into standard…
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 present a quantum algorithmic routine that extends the realm of Grover-based heuristics for tackling combinatorial optimization problems with arbitrary efficiently computable objective and constraint functions. Building on previously…
The paper presents a comprehensive performance evaluation of some heuristic search algorithms in the context of autonomous systems and robotics. The objective of the study is to evaluate and compare the performance of different search…
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…
A subgradient method is presented for solving general convex optimization problems, the main requirement being that a strictly-feasible point is known. A feasible sequence of iterates is generated, which converges to within user-specified…
Bayesian optimization works effectively optimizing parameters in black-box problems. However, this method did not work for high-dimensional parameters in limited trials. Parameters can be efficiently explored by nonlinearly embedding them…