Related papers: An adaptive discretization method solving semi-inf…
Semidefinite relaxations are widely used to compute upper bounds on the objective of optimization problems involving noncommutative polynomials. Such optimization problems are prevalent in quantum information. We present an algorithm able…
We study the optimization of the expected long-term reward in finite partially observable Markov decision processes over the set of stationary stochastic policies. In the case of deterministic observations, also known as state aggregation,…
In this paper, an efficient parallel splitting method is proposed for the optimal control problem with parabolic equation constraints. The linear finite element is used to approximate the state variable and the control variable in spatial…
In this paper, we propose a multilevel stochastic framework for the solution of nonconvex unconstrained optimization problems. The proposed approach uses random regularized first-order models that exploit an available hierarchical…
We suggest an adaptive version of a partial linearization method for composite optimization problems. The goal function is the sum of a smooth function and a non necessary smooth convex separable function, whereas the feasible set is the…
In this paper, a symmetrized two-scale finite element method is proposed for a class of partial differential equations with symmetric solutions. With this method, the finite element approximation on a fine tensor product grid is reduced to…
We present and analyze a central cutting surface algorithm for general semi-infinite convex optimization problems, and use it to develop a novel algorithm for distributionally robust optimization problems in which the uncertainty set…
When modeling scientific and industrial problems, geometries are typically modeled by explicit boundary representations obtained from computer-aided design software. Unfitted (also known as embedded or immersed) finite element methods offer…
Nonlinear optimal control problems for trajectory planning with obstacle avoidance present several challenges. While general-purpose optimizers and dynamic programming methods struggle when adopted separately, their combination enabled by a…
We consider the solution of nonlinear programs with nonlinear semidefiniteness constraints. The need for an efficient exploitation of the cone of positive semidefinite matrices makes the solution of such nonlinear semidefinite programs more…
A type of adaptive finite element method for the eigenvalue problems is proposed based on the multilevel correction scheme. In this method, adaptive finite element method to solve eigenvalue problems involves solving associated boundary…
In this paper we investigate how standard nonlinear programming algorithms can be used to solve constrained optimization problems in a distributed manner. The optimization setup consists of a set of agents interacting through a…
We propose an algorithm for solving bound-constrained mathematical programs with complementarity constraints on the variables. Each iteration of the algorithm involves solving a linear program with complementarity constraints in order to…
We present an accurate and efficient discretization approach for the adaptive discretization of typical model equations employed in numerical weather prediction. A semi-Lagrangian approach is combined with the TR-BDF2 semi-implicit time…
We develop a hybrid spatial discretization for the wave equation in second order form, based on high-order accurate finite difference methods and discontinuous Galerkin methods. The hybridization combines computational efficiency of finite…
This paper addresses the optimal covariance steering problem for stochastic discrete-time linear systems subject to probabilistic state and control constraints. A method is presented for efficiently attaining the exact solution of the…
We present a continuous finite element method for some examples of fully nonlinear elliptic equation. A key tool is the discretisation proposed in Lakkis & Pryer (2011, SISC) allowing us to work directly on the strong form of a linear PDE.…
Bilevel optimization problems are a class of challenging optimization problems, which contain two levels of optimization tasks. In these problems, the optimal solutions to the lower level problem become possible feasible candidates to the…
We consider a linear-quadratic elliptic optimal control problem with point evaluations of the state variable in the cost functional. The state variable is discretized by conforming linear finite elements. For control discretization, three…
In this paper, we study randomized and cyclic coordinate descent for convex unconstrained optimization problems. We improve the known convergence rates in some cases by using the numerical semidefinite programming performance estimation…