Related papers: Cutting plane methods with gradient-based heuristi…
Many high-dimensional optimisation problems exhibit rich geometric structures in their set of minimisers, often forming smooth manifolds due to over-parametrisation or symmetries. When this structure is known, at least locally, it can be…
In this paper we consider large-scale smooth optimization problems with multiple linear coupled constraints. Due to the non-separability of the constraints, arbitrary random sketching would not be guaranteed to work. Thus, we first…
We propose new sequential simulation-optimization algorithms for general convex optimization via simulation problems with high-dimensional discrete decision space. The performance of each choice of discrete decision variables is evaluated…
In this work, solution of the finite horizon hybrid optimal control problem as the central element of the receding horizon optimal control (model predictive control) is investigated based on the indirect approach. The response of a hybrid…
Recent progress in deep learning has been driven by increasingly larger models. However, their computational and energy demands have grown proportionally, creating significant barriers to their deployment and to a wider adoption of deep…
We report a computational study of cutting plane algorithms for multi-stage stochastic mixed-integer programming models with the following cuts: (i) Benders', (ii) Integer L-shaped, and (iii) Lagrangian cuts. We first show that Integer…
We present a geometric multilevel optimization approach that smoothly incorporates box constraints. Given a box constrained optimization problem, we consider a hierarchy of models with varying discretization levels. Finer models are…
The cutting plane approach to optimal matchings has been discussed by several authors over the past decades (e.g., Padberg and Rao '82, Grotschel and Holland '85, Lovasz and Plummer '86, Trick '87, Fischetti and Lodi '07) and its…
The global optimization literature places large emphasis on reducing intractable optimization problems into more tractable structured optimization forms. In order to achieve this goal, many existing methods are restricted to optimization…
Variable order structures model situations in which the comparison between two points depends on a point-to-cone map. In this paper, an inexact projected gradient method for solving smooth constrained vector optimization problems on…
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…
Stochastic nonconvex optimization problems with nonlinear constraints have a broad range of applications in intelligent transportation, cyber-security, and smart grids. In this paper, first, we propose an inexact-proximal accelerated…
Projection methods are popular algorithms for iteratively solving feasibility problems in Euclidean or even Hilbert spaces. They employ (selections of) nearest point mappings to generate sequences that are designed to approximate a point in…
Suppose that there is a ground set which consists of a large number of vectors in a Hilbert space. Consider the problem of selecting a subset of the ground set such that the projection of a vector of interest onto the subspace spanned by…
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…
This paper is devoted to the theoretical and numerical investigation of an augmented Lagrangian method for the solution of optimization problems with geometric constraints. Specifically, we study situations where parts of the constraints…
This paper proposes and develops new Newton-type methods to solve structured nonconvex and nonsmooth optimization problems with justifying their fast local and global convergence by means of advanced tools of variational analysis and…
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…
Many problems of theoretical and practical interest involve finding an optimum over a family of convex functions. For instance, finding the projection on the convex functions in $H^k(\Omega)$, and optimizing functionals arising from some…
A stochastic gradient method for finite-sum minimization subject to deterministic linear constraints is proposed and analyzed. The procedure presented adapts the projected gradient method on convex set to the use of both a stochastic…