Related papers: A Study on the Algorithm and Implementation of SDP…
This manuscript describes a method for training linear SVMs (including binary SVMs, SVM regression, and structural SVMs) from large, out-of-core training datasets. Current strategies for large-scale learning fall into one of two camps;…
We propose a homogeneous primal-dual interior-point method to solve sum-of-squares optimization problems by combining non-symmetric conic optimization techniques and polynomial interpolation. The approach optimizes directly over the…
The aim of this paper is to solve linear semidefinite programs arising from higher-order Lasserre relaxations of unconstrained binary quadratic optimization problems. For this we use an interior point method with a preconditioned conjugate…
The aim of this paper is to solve large-and-sparse linear Semidefinite Programs (SDPs) with low-rank solutions. We propose to use a preconditioned conjugate gradient method within second-order SDP algorithms and introduce a new efficient…
This paper introduces a novel Differential Dynamic Programming (DDP) algorithm for solving discrete-time finite-horizon optimal control problems with inequality constraints. Two variants, namely Feasible- and Infeasible-IPDDP algorithms,…
Many problems of systems control theory boil down to solving polynomial equations, polynomial inequalities or polyomial differential equations. Recent advances in convex optimization and real algebraic geometry can be combined to generate…
In practice, non-specialized interior point algorithms often cannot utilize the massively parallel compute resources offered by modern many- and multi-core compute platforms. However, efficient distributed solution techniques are required,…
In this work, we propose a new local optimization method to solve a class of nonconvex semidefinite programming (SDP) problems. The basic idea is to approximate the feasible set of the nonconvex SDP problem by inner positive semidefinite…
Non-commutative polynomial optimization is a powerful technique with numerous applications in quantum nonlocality, quantum key distribution, causal inference, many-body physics, amongst others. The standard approach is to reduce such…
We propose a new homotopy-based conditional gradient method for solving convex optimization problems with a large number of simple conic constraints. Instances of this template naturally appear in semidefinite programming problems arising…
An algorithm based on the interior-point methodology for solving continuous nonlinearly constrained optimization problems is proposed, analyzed, and tested. The distinguishing feature of the algorithm is that it presumes that only noisy…
Thermodynamic computing has emerged as a promising paradigm for accelerating computation by harnessing the thermalization properties of physical systems. This work introduces a novel approach to solving quadratic programming problems using…
In this paper we generalize the Interior Point-Proximal Method of Multipliers (IP-PMM) presented in [An Interior Point-Proximal Method of Multipliers for Convex Quadratic Programming, Computational Optimization and Applications, 78,…
With the surge of multi- and manycores, much research has focused on algorithms for mapping and scheduling on these complex platforms. Large classes of these algorithms face scalability problems. This is why diverse methods are commonly…
In this paper we propose a set of guidelines to select a solver for the solution of nonlinear programming problems. With this in mind, we present a comparison of the convergence performances of commonly used solvers for both unconstrained…
Semidefinite programs (SDPs) can be solved in polynomial time by interior point methods, but scalability can be an issue. To address this shortcoming, over a decade ago, Burer and Monteiro proposed to solve SDPs with few equality…
This paper presents a novel method for solving partial differential equations on three-dimensional CAD geometries by means of immersed isogeometric discretizations that do not require quadrature schemes. It relies on a new developed…
Support vector machines (SVMs) are well-studied supervised learning models for binary classification. In many applications, large amounts of samples can be cheaply and easily obtained. What is often a costly and error-prone process is to…
A stochastic-gradient-based interior-point algorithm for minimizing a continuously differentiable objective function (that may be nonconvex) subject to bound constraints is presented, analyzed, and demonstrated through experimental results.…
Designing the topology of three-dimensional structures is a challenging problem due to its memory and time consumption. In this paper, we present a robust and efficient algorithm for solving large-scale 3D topology optimization problems.…