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In this paper we explore the role of duality principles within the problem of rotation averaging, a fundamental task in a wide range of computer vision applications. In its conventional form, rotation averaging is stated as a minimization…
Operator splitting schemes are a class of powerful algorithms that solve complicated monotone inclusion and convex optimization problems that are built from many simpler pieces. They give rise to algorithms in which all simple pieces of the…
The alternating direction multiplier method (ADMM) is widely used in computer graphics for solving optimization problems that can be nonsmooth and nonconvex. It converges quickly to an approximate solution, but can take a long time to…
A distributed nonsmooth robust resource allocation problem with cardinality constrained uncertainty is investigated in this paper. The global objective is consisted of local objectives, which are convex but nonsmooth. Each agent is…
This paper revisits the well-studied fixed point problem from a unified viewpoint of mathematical modeling and canonical duality theory, i.e. the original problem is first reformulated as a nonconvex optimization problem, its well-posedness…
We show that a broad range of convex optimization algorithms, including alternating projection, operator splitting, and multiplier methods, can be systematically derived from the framework of subspace correction methods via convex duality.…
We present new algorithms to perform fast probabilistic collision queries between convex as well as non-convex objects. Our approach is applicable to general shapes, where one or more objects are represented using Gaussian probability…
Preliminary results of our investigations on solving indefinite qua\-dra\-tic programs by dynamical systems are given. First, dynamical systems corresponding to two fundamental DC programming algorithms to deal with indefinite quadratic…
Rapid advances in data collection and processing capabilities have allowed for the use of increasingly complex models that give rise to nonconvex optimization problems. These formulations, however, can be arbitrarily difficult to solve in…
In this paper a class of robust two-stage combinatorial optimization problems is discussed. It is assumed that the uncertain second stage costs are specified in the form of a convex uncertainty set, in particular polyhedral or ellipsoidal…
This paper investigates a specific class of nonsmooth nonconvex optimization problems in the face of data uncertainty, namely, robust optimization problems, where the given objective function can be expressed as a difference of two…
An iterative formula based on Newton Method alone is presented for the iterative solutions of equations that ensures convergence in cases where the traditional Newton Method may fail to converge to the desired root. In addition, the method…
This paper studies a class of monotone inclusion problems in a real Hilbert space involving the sum of three operators, where two are maximal monotone and the third is cocoercive. The Davis--Yin three-operator splitting method extends the…
We introduce a new second order stochastic algorithm to estimate the entropically regularized optimal transport cost between two probability measures. The source measure can be arbitrary chosen, either absolutely continuous or discrete,…
We consider distributed optimization in the client-server setting. By use of Douglas-Rachford splitting to the dual of the sum problem, we design a BFGS method that requires minimal communication (sending/receiving one vector per round for…
Continuous optimization is an important problem in many areas of AI, including vision, robotics, probabilistic inference, and machine learning. Unfortunately, most real-world optimization problems are nonconvex, causing standard convex…
The distributed dual ascent is an established algorithm to solve strongly convex multi-agent optimization problems with separable cost functions, in the presence of coupling constraints. In this paper, we study its asynchronous counterpart.…
Robust and distributionally robust optimization are modeling paradigms for decision-making under uncertainty where the uncertain parameters are only known to reside in an uncertainty set or are governed by any probability distribution from…
We propose a DC proximal Newton algorithm for solving nonconvex regularized sparse learning problems in high dimensions. Our proposed algorithm integrates the proximal Newton algorithm with multi-stage convex relaxation based on the…
This paper proposes a nonmonotone proximal quasi-Newton algorithm for unconstrained convex multiobjective composite optimization problems. To design the search direction, we minimize the max-scalarization of the variations of the Hessian…