Related papers: Scaling the semidefinite program solver SDPB

The family of Multiscale Hybrid-Mixed (MHM) finite element methods has received considerable attention from the mathematics and engineering community in the last few years. The MHM methods allow solving highly heterogeneous problems on…

Partial differential equations (PDEs) are crucial in modeling diverse phenomena across scientific disciplines, including seismic and medical imaging, computational fluid dynamics, image processing, and neural networks. Solving these PDEs at…

This paper proposes a squared smoothing Newton method via the Huber smoothing function for solving semidefinite programming problems (SDPs). We first study the fundamental properties of the matrix-valued mapping defined upon the Huber…

A weakly infeasible semidefinite program (SDP) has no feasible solution, but it has approximate solutions whose constraint violation is arbitrarily small. These SDPs are ill-posed and numerically often unsolvable. They are also closely…

As spiking-based deep learning inference applications are increasing in embedded systems, these systems tend to integrate neuromorphic accelerators such as $\mu$Brain to improve energy efficiency. We propose a $\mu$Brain-based scalable…

Symmetric positive semidefinite (SPSD) matrix approximation is an important problem with applications in kernel methods. However, existing SPSD matrix approximation methods such as the Nystr\"om method only have weak error bounds. In this…

We show {\it semidefinite programming} (SDP) feasibility problem is equivalent to solving a {\it convex hull relaxation} (CHR) for a finite system of quadratic equations. On the one hand, this offers a simple description of SDP. On the…

This paper introduces a new approximation scheme for solving high-dimensional semilinear partial differential equations (PDEs) and backward stochastic differential equations (BSDEs). First, we decompose a target semilinear PDE (BSDE) into…

Nowadays, it has become a basic need to reuse existing Application Programming Interface (API), Class Libraries, and frameworks for rapid software development. Software developers often reuse this by calling the respective APIs or…

We present a semidefinite program (SDP) algorithm to find eigenvalues of Schr\"{o}dinger operators within the bootstrap approach to quantum mechanics. The bootstrap approach involves two ingredients: a nonlinear set of constraints on the…

In this paper, we propose a new sequential quadratic semidefinite programming (SQSDP) method for solving degenerate nonlinear semidefinite programs (NSDPs), in which we produce iteration points by solving a sequence of stabilized quadratic…

Fast power system state estimation (SE) solution is of paramount importance for achieving real-time decision making in power grid operations. Semidefinite programming (SDP) reformulation has been shown effective to obtain the global optimum…

In this era of diverse and heterogeneous computer architectures, the programmability issues, such as productivity and portable efficiency, are crucial to software development and algorithm design. One way to approach the problem is to step…

Exploiting sparsity in Semidefinite Programs (SDP) is critical to solving large-scale problems. The chordal completion based maximal clique decomposition is the preferred approach for exploiting sparsity in SDPs. In this paper, we show that…

In semidefinite programming (SDP), unlike in linear programming, Farkas' lemma may fail to prove infeasibility. Here we obtain an exact, short certificate of infeasibility in SDP by an elementary approach: we reformulate any semidefinite…

In this paper, we propose an efficient semidefinite programming (SDP) approach to worst-case linear discriminant analysis (WLDA). Compared with the traditional LDA, WLDA considers the dimensionality reduction problem from the worst-case…

Many real-life problems of practical importance -- spanning a wide range of applications from chip design to bioinformatics -- represent constraint satisfaction problems, where classical solvers have to rely on heuristic approximations due…

Semidefinite programs (SDPs) are powerful theoretical tools that have been studied for over two decades, but their practical use remains limited due to computational difficulties in solving large-scale, realistic-sized problems. In this…

A new approach to solving a class of rankconstrained semi-definite programming (SDP) problems, which appear in many signal processing applications such as transmit beamspace design in multiple-input multiple-output (MIMO) radar, downlink…

While semidefinite programming (SDP) problems are polynomially solvable in theory, it is often difficult to solve large SDP instances in practice. One technique to address this issue is to relax the global positive-semidefiniteness (PSD)…