Related papers: Geodesic and Contour Optimization Using Conformal …

Non-convex optimization is ubiquitous in modern machine learning. Researchers devise non-convex objective functions and optimize them using off-the-shelf optimizers such as stochastic gradient descent and its variants, which leverage the…

The traditional way of tackling discrete optimization problems is by using local search on suitably defined cost or fitness landscapes. Such approaches are however limited by the slowing down that occurs when the local minima that are a…

In this paper, an efficient modified Newton type algorithm is proposed for nonlinear unconstrianed optimization problems. The modified Hessian is a convex combination of the identity matrix (for steepest descent algorithm) and the Hessian…

We present a general numerical approach to shape optimization with state constraints for 2-dimensional geometries, without relaxing the constraints. To do this we reformulate the problem on a fixed reference domain using a conformal…

Consider convex optimization problems subject to a large number of constraints. We focus on stochastic problems in which the objective takes the form of expected values and the feasible set is the intersection of a large number of convex…

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…

The conjugate function method is an algorithm for numerical computation of conformal mappings for simply and multiply connected domains on surfaces. In this paper the conjugate function method, earlier used for simply connected domains, is…

This paper concerns models and convergence principles for dealing with stochasticity in a wide range of algorithms arising in nonlinear analysis and optimization in Hilbert spaces. It proposes a flexible geometric framework within which…

This paper proposes and justifies two globally convergent Newton-type methods to solve unconstrained and constrained problems of nonsmooth optimization by using tools of variational analysis and generalized differentiation. Both methods are…

In this work, we analyze the global convergence property of coordinate gradient descent with random choice of coordinates and stepsizes for non-convex optimization problems. Under generic assumptions, we prove that the algorithm iterate…

Genetic algorithms are a powerful tool in optimization for single and multi-modal functions. This paper provides an overview of their fundamentals with some analytical examples. In addition, we explore how they can be used as a parameter…

We present a novel formulation of ergodic trajectory optimization that can be specified over general domains using kernel maximum mean discrepancy. Ergodic trajectory optimization is an effective approach that generates coverage paths for…

Numerous applications require algorithms that can align partially overlapping point sets while maintaining invariance to geometric transformations (e.g., similarity, affine, rigid). This paper introduces a novel global optimization method…

Random search methods are widely used for global optimization due to their theoretical generality and implementation simplicity. This paper proposes a depth-first directional search (DFDS) algorithm for globally solving nonconvex…

We provide preliminary details and formulation of an optimization strategy under current development that is able to automatically tune the parameters of a Support Vector Machine over new datasets. The optimization strategy is a heuristic…

We propose a random coordinate descent algorithm for optimizing a non-convex objective function subject to one linear constraint and simple bounds on the variables. Although it is common use to update only two random coordinates…

Recent studies have shown that many nonconvex machine learning problems satisfy a generalized-smooth condition that extends beyond traditional smooth nonconvex optimization. However, the existing algorithms are not fully adapted to such…

We extend the standard notion of self-concordance to non-convex optimization and develop a family of second-order algorithms with global convergence guarantees. In particular, two function classes -- \textit{weakly self-concordant}…

Real-time motion planning is a vital function of robotic systems. Different from existing roadmap algorithms which first determine the free space and then determine the collision-free path, researchers recently proposed several convex…

The increasing availability of graph-structured data motivates the task of optimising over functions defined on the node set of graphs. Traditional graph search algorithms can be applied in this case, but they may be sample-inefficient and…