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A step-truncated method in a wide neighborhood interior-point algorithm for linear programming
In path-following interior-point algorithms, the predictor–corrector algorithms have quadratic convergence for the nondegenerate case, such that the...
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Error analysis of discontinuous Galerkin methods on layer adapted meshes for two dimensional turning point problem
A class of two-dimensional singularly perturbed convection–diffusion problems with turning points is studied in this work. Since the turning point...
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Complexity Analysis of a Full-Newton Step Interior-Point Method for Monotone Weighted Linear Complementarity Problems
In this paper, we present a full-Newton step interior-point method for solving monotone Weighted Linear Complementarity Problem. We use the technique...
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A polynomial time infeasible interior-point arc-search algorithm for convex optimization
This paper proposes an infeasible interior-point algorithm for the convex optimization problem using arc-search techniques. The proposed algorithm...
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A limiting analysis on regularization of singular SDP and its implication to infeasible interior-point algorithms
We consider primal-dual pairs of semidefinite programs and assume that they are singular, i.e., both primal and dual are either weakly feasible or...
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Interior Transmission Resonance
In this chapter, we consider the interior transmission eigenvalue problem. Our focus is on justifying that the transmission eigenfunctions form a...
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An interior-point algorithm for semidefinite least-squares problems
We propose a feasible primal-dual path-following interior-point algorithm for semidefinite least squares problems (SDLS). At each iteration, the...
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An Interior Point Parameterized Central Path Following Algorithm for Linearly Constrained Convex Programming
An interior point algorithm is proposed for linearly constrained convex programming following a parameterized central path, which is a generalization...
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An infeasible-start framework for convex quadratic optimization, with application to constraint-reduced interior-point and other methods
A framework is proposed for solving general convex quadratic programs (CQPs) from an infeasible starting point by invoking an existing feasible-start ...
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A Relaxed Interior Point Method for Low-Rank Semidefinite Programming Problems with Applications to Matrix Completion
A new relaxed variant of interior point method for low-rank semidefinite programming problems is proposed in this paper. The method is a step outside...
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Solving Multiobjective Environmentally Friendly and Economically Feasible Electric Power Distribution Problem by Primal-Dual Interior-Point Method
This paper introduces a primal-dual interior-point algorithm to obtain the Pareto optimal solutions for a multiobjective environmentally friendly and...
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Robust Interior Penalty Discontinuous Galerkin Methods
A new variant of the IPDG method is presented, involving carefully constructed weighted averages of the gradient of the approximate solution. The...
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Exact Controllability of Wave Equations with Interior Degeneracy and One-Sided Boundary Control
In this paper, the authors mainly consider the exact controllability for degenerate wave equation, which degenerates at the interior point, and...
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A new corrector–predictor interior-point method for symmetric cone optimization
In this work, we present a corrector–predictor interior-point method for symmetric cone optimization based on Euclidean Jordan algebras as a key...
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Approximate solution of system of equations arising in interior-point methods for bound-constrained optimization
The focus in this paper is interior-point methods for bound-constrained nonlinear optimization, where the system of nonlinear equations that arise...
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Interior Point Methods Adapted to Improper Linear Programs
For linear programs, we consider schemes for the formation of a generalized central path, which arise under the simultaneous use of interior and...
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Singular perturbation boundary and interior layers problems with multiple turning points
In the study of singularly perturbed boundary problems with turning points, the solution undergoes sharp changes near these points and exhibits...
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An Interior Point-Proximal Method of Multipliers for Linear Positive Semi-Definite Programming
In this paper we generalize the Interior Point-Proximal Method of Multipliers (IP-PMM) presented in Pougkakiotis and Gondzio (Comput Optim Appl...
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Novel Kernel Function With a Hyperbolic Barrier Term to Primal-dual Interior Point Algorithm for SDP Problems
In this paper, we introduce for the first time a new eligible kernel function with a hyperbolic barrier term for semidefinite programming (SDP). This...
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Modified controlled Cholesky factorization for preconditioning linear systems from the interior-point method
The interior-point method solves large linear programming problems in a few iterations. Each iteration requires computing the solution to one or more...
