Related papers: Comments to Symmetrical Smoothing Method and First…
A common problem in the optimization of structures is the handling of uncertainties in the parameters. If the parameters appear in the constraints, the uncertainties can lead to an infinite number of constraints. Usually the constraints…
Edge-preserving smoothing (EPS) can be formulated as minimizing an objective function that consists of data and prior terms. This global EPS approach shows better smoothing performance than a local one that typically has a form of weighted…
In this paper, we consider the minimization of a $C^2-$smooth and strongly convex objective depending on a given parameter, which is usually found in many practical applications. We suppose that we desire to solve the problem with some…
An asymptotically optimal sampling-based planner employs sampling to solve robot motion planning problems and returns paths with a cost that converges to the optimal solution cost, as the number of samples approaches infinity. This…
Symmetry is a powerful tool for finding analytical solutions to differential equations, both partial and ordinary, via the similarity variables or via the invariance of the equation under group transformations. It is the largest group of…
We describe a novel optimization method for finite sums (such as empirical risk minimization problems) building on the recently introduced SAGA method. Our method achieves an accelerated convergence rate on strongly convex smooth problems.…
In this paper, we present a new stochastic algorithm, namely the stochastic block mirror descent (SBMD) method for solving large-scale nonsmooth and stochastic optimization problems. The basic idea of this algorithm is to incorporate the…
Randomized smoothing is sound when using infinite precision. However, we show that randomized smoothing is no longer sound for limited floating-point precision. We present a simple example where randomized smoothing certifies a radius of…
Polyhedral surfaces are fundamental objects in architectural geometry and industrial design. Whereas closeness of a given mesh to a smooth reference surface and its suitability for numerical simulations were already studied extensively, the…
This book is devoted to finite-dimensional problems of non-convex non-smooth optimization and numerical methods for their solution. The problem of nonconvexity is studied in the book on two main models of nonconvex dependencies: these are…
Why are simple, regular, and symmetric shapes common in nature? Many natural shapes arise as solutions to energy minimisation or other optimisation problems, but is there a general relation between optima and simple, regular shapes and…
We investigate the concept of symmetry and its role in problem solving. This paper first defines precisely the elements that constitute a "problem" and its "solution," and gives several examples to illustrate these definitions. Given…
We explore a new general-purpose heuristic for finding high-quality solutions to hard optimization problems. The method, called extremal optimization, is inspired by self-organized criticality, a concept introduced to describe emergent…
A Support Vector Method for multivariate performance measures was recently introduced by Joachims (2005). The underlying optimization problem is currently solved using cutting plane methods such as SVM-Perf and BMRM. One can show that these…
We consider stochastic optimization problems which use observed data to estimate essential characteristics of the random quantities involved. Sample average approximation (SAA) or empirical (plug-in) estimation are very popular ways to use…
We develop a globalized Proximal Newton method for composite and possibly non-convex minimization problems in Hilbert spaces. Additionally, we impose less restrictive assumptions on the composite objective functional considering…
We present a method of exploiting symmetries of discrete-time optimal control problems to reduce the dimensionality of dynamic programming iterations. The results are derived for systems with continuous state variables, and can be applied…
We consider the problem of minimizing a sum of several convex non-smooth functions. We introduce a new algorithm called the selective linearization method, which iteratively linearizes all but one of the functions and employs simple…
In this paper, the problem of computing the projection, and therefore the minimum distance, from a point onto a Minkowski sum of general convex sets is studied. Our approach is based on the minimum norm duality theorem originally stated by…
Parallel and cyclic projection algorithms are proposed for minimizing the sum of a finite family of convex functions over the intersection of a finite family of closed convex subsets of a Hilbert space. These algorithms are of…