Related papers: A hybrid constraint programming and semidefinite p…

Semidefinite programming is an indispensable tool in computer vision, but general-purpose solvers for semidefinite programs are often too slow and memory intensive for large-scale problems. We propose a general framework to approximately…

We model the cardinality-constrained portfolio problem using semidefinite matrices and investigate a relaxation using semidefinite programming. Experimental results show that this relaxation generates tight lower bounds and even achieves…

We consider the stability analysis of a large class of linear 1-D PDEs with polynomial data. This class of PDEs contains, as examples, parabolic and hyperbolic PDEs, PDEs with boundary feedback and systems of in-domain/boundary coupled…

We consider the problem of approximating the reachable set of a discrete-time polynomial system from a semialgebraic set of initial conditions under general semialgebraic set constraints. Assuming inclusion in a given simple set like a box…

We build on a recently proposed method for explaining solutions of constraint satisfaction problems. An explanation here is a sequence of simple inference steps, where the simplicity of an inference step is measured by the number and types…

We develop a machine-learning framework to learn hyperparameter sequences for accelerated first-order methods (e.g., the step size and momentum sequences in accelerated gradient descent) to quickly solve parametric convex optimization…

In this paper, we propose and analyze a fast two-point gradient algorithm for solving nonlinear ill-posed problems, which is based on the sequential subspace optimization method. A complete convergence analysis is provided under the…

We consider the stability and the input-output analysis problems of a class of large-scale hybrid systems composed of continuous dynamics coupled with discrete dynamics defined over finite alphabets, e.g., deterministic finite state…

This paper develops a new storage-optimal algorithm that provably solves generic semidefinite programs (SDPs) in standard form. This method is particularly effective for weakly constrained SDPs. The key idea is to formulate an approximate…

We derive a stochastic gradient algorithm for semidefinite optimization using randomization techniques. The algorithm uses subsampling to reduce the computational cost of each iteration and the subsampling ratio explicitly controls…

To address difficult optimization problems, convex relaxations based on semidefinite programming are now common place in many fields. Although solvable in polynomial time, large semidefinite programs tend to be computationally challenging.…

One of the most important problems in hybrid systems is the {\em reachability problem}. The reachability problem has been shown to be undecidable even for a subclass of {\em linear} hybrid systems. In view of this, the main focus in the…

This paper develops a unified methodology for probabilistic analysis and optimal control design for jump diffusion processes defined by polynomials. For such systems, the evolution of the moments of the state can be described via a system…

In this paper we propose a new method to stabilise non-symmetric indefinite problems. The idea is to solve a forward and an adjoint problem simultaneously using a suitable stabilised finite element method. Both stabilisation of the element…

We present a new generic approach to the condensed-matter ground-state problem which is complementary to variational techniques and works directly in the thermodynamic limit. Relaxing the ground-state problem, we obtain semidefinite…

In this work we study binary classification problems where we assume that our training data is subject to uncertainty, i.e. the precise data points are not known. To tackle this issue in the field of robust machine learning the aim is to…

In this paper we consider stable matchings subject to assignment constraints. These are matchings that require certain assigned pairs to be included, insist that some other assigned pairs are not, and, importantly, are stable. Our main…

In this paper we present a new semidefinite programming hierarchy for covering problems in compact metric spaces. Over the last years, these kind of hierarchies were developed primarily for geometric packing and for energy minimization…

Prediction+optimization is a common real-world paradigm where we have to predict problem parameters before solving the optimization problem. However, the criteria by which the prediction model is trained are often inconsistent with the goal…

Dynamic programming (DP) is an algorithmic design paradigm for the efficient, exact solution of otherwise intractable, combinatorial problems. However, DP algorithm design is often presented in an ad-hoc manner. It is sometimes difficult to…