Related papers: Continuation Path Learning for Homotopy Optimizati…
Implicit inverse problems, in which noisy observations of a physical quantity are used to infer a nonlinear functional applied to an associated function, are inherently ill posed and often exhibit non uniqueness of solutions. Such problems…
This paper presents a systematic approach for computing local solutions to motion planning problems in non-convex environments using numerical optimal control techniques. It extends the range of use of state-of-the-art numerical optimal…
The concept of path homotopy has received widely attention in the field of path planning in recent years. In this article, a homotopy invariant based on convex dissection for a two-dimensional bounded Euclidean space is developed, which can…
Efficient planning in dynamic and uncertain environments is a fundamental challenge in robotics. In the context of trajectory optimization, the feasibility of paths can change as the environment evolves. Therefore, it can be beneficial to…
Large-scale strongly nonlinear and nonconvex mixed-integer nonlinear programming (MINLP) models frequently appear in optimisation-based process synthesis, integration, intensification, and process control. However, they are usually…
The objective function used in trajectory optimization is often non-convex and can have an infinite set of local optima. In such cases, there are diverse solutions to perform a given task. Although there are a few methods to find multiple…
A special homotopy continuation method, as a combination of the polyhedral homotopy and the linear product homotopy, is proposed for computing all the isolated solutions to a special class of polynomial systems. The root number bound of…
We develop a homotopy-based framework for computing Karush-Kuhn-Tucker (KKT) points of multiobjective optimization problems. The proposed homotopy map continuously deforms an easily solvable system into the KKT conditions associated with…
We propose a sequential homotopy method for the solution of mathematical programming problems formulated in abstract Hilbert spaces under the Guignard constraint qualification. The method is equivalent to performing projected backward Euler…
In this extended abstract, we report on ongoing work towards an approximate multimodal optimization algorithm with asymptotic guarantees. Multimodal optimization is the problem of finding all local optimal solutions (modes) to a path…
Despite the recent progress in hyperparameter optimization (HPO), available benchmarks that resemble real-world scenarios consist of a few and very large problem instances that are expensive to solve. This blocks researchers and…
We use our recent implementation of a certified homotopy tracking algorithm to search for start systems that minimize the average complexity of finding all roots of a regular system of polynomial equations. While finding optimal start…
Traditional maximum entropy and sparsity-based algorithms for analytic continuation often suffer from the ill-posed kernel matrix or demand tremendous computation time for parameter tuning. Here we propose a neural network method by convex…
The classical homotopy optimization approach has the potential to deal with highly nonlinear landscape, such as the energy landscape of QAOA problems. Following this motivation, we introduce Hamiltonian-Oriented Homotopy QAOA (HOHo-QAOA),…
First-order stochastic methods for solving large-scale non-convex optimization problems are widely used in many big-data applications, e.g. training deep neural networks as well as other complex and potentially non-convex machine learning…
A method for solving zero-finding problems is developed by tracking homotopy paths, which define connecting channels between an auxiliary problem and the objective problem. Current algorithms' success highly relies on empirical knowledge,…
This paper suggests two novel ideas to develop new proximal variable-metric methods for solving a class of composite convex optimization problems. The first idea is a new parameterization of the optimality condition which allows us to…
One method to solve expensive black-box optimization problems is to use a surrogate model that approximates the objective based on previous observed evaluations. The surrogate, which is cheaper to evaluate, is optimized instead to find an…
In this article, we introduce a new homotopy function to trace the trajectory by applying modified homotopy continuation method for finding the solution of the linear complementarity problem. Earlier several authors attempted to propose…
This paper presents a computationally efficient optimization algorithm for solving nonconvex optimal control problems that involve discrete logic constraints. Traditional solution methods for these constraints require binary variables and…