Related papers: Optimal Preconditioning for Online Quadratic Cone …
We consider the minimization of a continuous function over the intersection of a regular cone with an affine set via a new class of adaptive first- and second-order optimization methods, building on the Hessian-barrier techniques introduced…
Constraint programming (CP) is a powerful technique for solving constraint satisfaction and optimization problems. In CP solvers, the variable ordering strategy used to select which variable to explore first in the solving process has a…
Robust optimization is a common framework in optimization under uncertainty when the problem parameters are not known, but it is rather known that the parameters belong to some given uncertainty set. In the robust optimization framework the…
This paper studies first-order algorithms for solving fully composite optimization problems over convex and compact sets. We leverage the structure of the objective by handling its differentiable and non-differentiable components…
Nonlinear model predictive control (NMPC) often requires real-time solution to optimization problems. However, in cases where the mathematical model is of high dimension in the solution space, e.g. for solution of partial differential…
We present a hybrid algorithm for optimizing a convex, smooth function over the cone of positive semidefinite matrices. Our algorithm converges to the global optimal solution and can be used to solve general large-scale semidefinite…
We consider a linear iterative solver for large scale linearly constrained quadratic minimization problems that arise, for example, in optimization with PDEs. By a primal-dual projection (PDP) iteration, which can be interpreted and…
We consider a convex minimization problem for which the objective is the sum of a homogeneous polynomial of degree four and a linear term. Such task arises as a subproblem in algorithms for quadratic inverse problems with a…
This paper presents new first-order methods for achieving optimal oracle complexities in convex optimization with convex functional constraints. Oracle complexities are measured by the number of function and gradient evaluations. To achieve…
We consider optimization problems with manifold-valued constraints. These generalize classical equality and inequality constraints to a setting in which both the domain and the codomain of the constraint mapping are smooth manifolds. We…
In this paper we present a new algorithmic realization of a projection-based scheme for general convex constrained optimization problem. The general idea is to transform the original optimization problem to a sequence of feasibility…
Non-prehensile manipulation in high-dimensional systems is challenging for a variety of reasons. One of the main reasons is the computationally long planning times that come with a large state space. Trajectory optimisation algorithms have…
Accelerated first order methods, also called fast gradient methods, are popular optimization methods in the field of convex optimization. However, they are prone to suffer from oscillatory behaviour that slows their convergence when medium…
Convex optimization problems arising in applications often have favorable objective functions and complicated constraints, thereby precluding first-order methods from being immediately applicable. We describe an approach that exchanges the…
Two approximation algorithms for solving convex vector optimization problems (CVOPs) are provided. Both algorithms solve the CVOP and its geometric dual problem simultaneously. The first algorithm is an extension of Benson's outer…
In this paper, we address the efficient numerical solution of linear and quadratic programming problems, often of large scale. With this aim, we devise an infeasible interior point method, blended with the proximal method of multipliers,…
Selecting the best hyperparameters for a particular optimization instance, such as the learning rate and momentum, is an important but nonconvex problem. As a result, iterative optimization methods such as hypergradient descent lack global…
We present two first-order, sequential optimization algorithms to solve constrained optimization problems. We consider a black-box setting with a priori unknown, non-convex objective and constraint functions that have Lipschitz continuous…
In this paper, we propose a new convergent conic programming hierarchy of relaxations involving both semi-definite cone and second-order cone constraints for solving nonconvex polynomial optimization problems to global optimality. The…
Convex nonsmooth optimization problems, whose solutions live in very high dimensional spaces, have become ubiquitous. To solve them, the class of first-order algorithms known as proximal splitting algorithms is particularly adequate: they…