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Introduction to Interior Point Methods
In this chapter we give a short introduction to interior point methods (IPMs). We start from early results given in the 1960s on barrier methods and...
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Riemannian Interior Point Methods for Constrained Optimization on Manifolds
We extend the classical primal-dual interior point method from the Euclidean setting to the Riemannian one. Our method, named the Riemannian interior...
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Interior-Point Methods
One of the most powerful methods for solving nonlinear optimization problems known as the interior-point method is to be presented in this chapter....
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Log-domain interior-point methods for convex quadratic programming
Applying an interior-point method to the central-path conditions is a widely used approach for solving quadratic programs. Reformulating these...
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General-purpose preconditioning for regularized interior point methods
In this paper we present general-purpose preconditioners for regularized augmented systems, and their corresponding normal equations, arising from...
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Newton and interior-point methods for (constrained) nonconvex–nonconcave minmax optimization with stability and instability guarantees
We address the problem of finding a local solution to a nonconvex–nonconcave minmax optimization using Newton type methods, including primal-dual...
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Accelerating Condensed Interior-Point Methods on SIMD/GPU Architectures
The interior-point method (IPM) has become the workhorse method for nonlinear programming. The performance of IPM is directly related to the linear...
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Recycling basic columns of the splitting preconditioner in interior point methods
Theoretical results and numerical experiments show that the linear systems originating from the last iterations of interior point methods (IPM) are...
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A structured modified Newton approach for solving systems of nonlinear equations arising in interior-point methods for quadratic programming
The focus in this work is on interior-point methods for inequality-constrained quadratic programs, and particularly on the system of nonlinear...
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Proximal Stabilized Interior Point Methods and Low-Frequency-Update Preconditioning Techniques
In this work, in the context of Linear and convex Quadratic Programming, we consider Primal Dual Regularized Interior Point Methods (PDR-IPMs) in the...
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An infeasible interior-point arc-search method with Nesterov’s restarting strategy for linear programming problems
An arc-search interior-point method is a type of interior-point method that approximates the central path by an ellipsoidal arc, and it can often...
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Set-Limited Functions and Polynomial-Time Interior-Point Methods
In this paper, we revisit some elements of the theory of self-concordant functions. We replace the notion of self-concordant barrier by a new notion...
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A projected-search interior-point method for nonlinearly constrained optimization
This paper concerns the formulation and analysis of a new interior-point method for constrained optimization that combines a shifted primal-dual...
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IPRSDP: a primal-dual interior-point relaxation algorithm for semidefinite programming
We propose an efficient primal-dual interior-point relaxation algorithm based on a smoothing barrier augmented Lagrangian, called IPRSDP, for solving...
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Block preconditioners for linear systems in interior point methods for convex constrained optimization
In this paper, we address the preconditioned iterative solution of the saddle-point linear systems arising from the (regularized) Interior Point...
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Complexity analysis of interior-point methods for second-order stationary points of nonlinear semidefinite optimization problems
We propose a primal-dual interior-point method (IPM) with convergence to second-order stationary points (SOSPs) of nonlinear semidefinite...
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A polynomial interior-point algorithm with improved iteration bounds for linear optimization
In this paper, we present a polynomial primal-dual interior-point algorithm for linear optimization based on a modified logarithmic barrier kernel...
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Frictionless Signorini’s Contact Problem for Hyperelastic Materials with Interior Point Optimizer
This paper presents a method to solve the mechanical problems undergoing finite deformations and the contact problems without friction, between an...
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Local convergence of primal–dual interior point methods for nonlinear semidefinite optimization using the Monteiro–Tsuchiya family of search directions
The recent advance of algorithms for nonlinear semidefinite optimization problems (NSDPs) is remarkable. Yamashita et al. first proposed a...
