Related papers: Structure Exploiting Interior Point Methods
This paper describes the implementation of a new interior point solver for linear programming for the open-source optimization library HiGHS. The solver uses a direct factorisation to solve the Newton systems, choosing the best approach…
Semidefinite programs (SDPs) are a fundamental class of optimization problems with important recent applications in approximation algorithms, quantum complexity, robust learning, algorithmic rounding, and adversarial deep learning. This…
In this paper, we put forth distributed algorithms for solving loosely coupled unconstrained and constrained optimization problems. Such problems are usually solved using algorithms that are based on a combination of decomposition and first…
Auxiliary variables are often used to model a convex piecewise linear function in the framework of linear optimization. This work shows that such variables yield a block diagonal plus low rank structure in the reduced KKT system of the dual…
The work of Wachter and Biegler suggests that infeasible-start interior point methods (IPMs) developed for linear programming cannot be adapted to nonlinear optimization without significant modification, i.e., using a two-phase or penalty…
The Interior-Point Methods are a class for solving linear programming problems that rely upon the solution of linear systems. At each iteration, it becomes important to determine how to solve these linear systems when the constraint matrix…
Point sets matching problems can be handled by optimal transport. The mechanism behind it is that optimal transport recovers the point-to-point correspondence associated with the least curl deformation. Optimal transport is a special form…
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.…
In this work, we introduce an interior-point method that employs tensor decompositions to efficiently represent and manipulate the variables and constraints of semidefinite programs, targeting problems where the solutions may not be…
Hierarchical least-squares programs with linear constraints (HLSP) are a type of optimization problem very common in robotics. Each priority level contains an objective in least-squares form which is subject to the linear constraints of the…
The AC Optimal Power Flow (AC-OPF) problem is a non-convex, NP-hard optimization task essential for secure and economic power system operation. While interior-point methods are widely used due to their computational efficiency, spatial…
We consider structured minimization problems subject to smooth inequality constraints and present a flexible algorithm that combines interior point (IP) and proximal gradient schemes. While traditional IP methods cannot cope with nonsmooth…
Optimization plays a central role in modern radiation therapy, where it is used to determine optimal treatment machine parameters in order to deliver precise doses adapted to each patient case. In general, solving the optimization problems…
We extend the classical primal-dual interior point method from the Euclidean setting to the Riemannian one. Our method, named the Riemannian interior point method, is for solving Riemannian constrained optimization problems. We establish…
Standard model predictive control strategies imply the online computation of control inputs at each sampling instance, which traditionally limits this type of control scheme to systems with slow dynamics. This paper focuses on distributed…
Quantum Interior Point Methods (QIPMs) have been attracting significant interests recently due to their potential of solving optimization problems substantially faster than state-of-the-art conventional algorithms. In general, QIPMs use…
We propose a primal-dual interior-point method (IPM) with convergence to second-order stationary points (SOSPs) of nonlinear semidefinite optimization problems, abbreviated as NSDPs. As far as we know, the current algorithms for NSDPs only…
A method is devised for numerically solving a class of finite-horizon optimal control problems subject to cascade linear discrete-time dynamics. It is assumed that the linear state and input inequality constraints, and the quadratic measure…
Beginning with the projectively invariant method for linear programming, interior point methods have led to powerful algorithms for many difficult computing problems, in combinatorial optimization, logic, number theory and non-convex…
The focus in this paper is interior-point methods for bound-constrained nonlinear optimization, where the system of nonlinear equations that arise are solved with Newton's method. There is a trade-off between solving Newton systems…