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The Entropic Barrier Is n-Self-Concordant
For any convex body \(K \subseteq \mathbb {R}^n\) , S....
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Optimal step length for the maximal decrease of a self-concordant function by the Newton method
In this paper we consider the problem of finding the optimal step length for the Newton method on the class of self-concordant functions, with the...
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On self-concordant barriers for generalized power cones
In the study of interior-point methods for nonsymmetric conic optimization and their applications, Nesterov (Optim Methods Softw 27(4–5): 893–917,...
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Generalized self-concordant analysis of Frank–Wolfe algorithms
Projection-free optimization via different variants of the Frank–Wolfe method has become one of the cornerstones of large scale optimization for...
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Optimal step length for the Newton method: case of self-concordant functions
The theoretical foundation of path-following methods is the performance analysis of the (damped) Newton step on the class of self-concordant...
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Self-Concordant Functions and IPM Complexity
The introduction by N. Karmarkar of his projective transformation method for LP in 1984; finding by P. Gill et al. (1986) of a, connection between...
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Convergence of a Weighted Barrier Algorithm for Stochastic Convex Quadratic Semidefinite Optimization
Mehrotra and Özevin (SIAM J Optim 19:1846–1880, 2009) computationally found that a weighted barrier decomposition algorithm for two-stage stochastic...
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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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Hessian barrier algorithms for non-convex conic optimization
A key problem in mathematical imaging, signal processing and computational statistics is the minimization of non-convex objective functions that may...
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Short-step methods are not strongly polynomial-time
Short-step methods are an important class of algorithms for solving convex constrained optimization problems. In this short paper, we show that under...
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Computing Conjugate Barrier Information for Nonsymmetric Cones
The recent interior point algorithm by Dahl and Andersen [
10 ] for nonsymmetric cones as well as earlier works [18 ,21 ] require derivative information...
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Sum of squares generalizations for conic sets
Polynomial nonnegativity constraints can often be handled using the sum of squares condition. This can be efficiently enforced using semidefinite...
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Performance enhancements for a generic conic interior point algorithm
In recent work, we provide computational arguments for expanding the class of proper cones recognized by conic optimization solvers, to permit...
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A Predictor-Corrector Algorithm for Semidefinite Programming that Uses the Factor Width Cone
We propose an interior point method (IPM) for solving semidefinite programming problems (SDPs). The standard interior point algorithms used to solve...
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Generalized self-concordant functions: a recipe for Newton-type methods
We study the smooth structure of convex functions by generalizing a powerful concept so-called self-concordance introduced by Nesterov and...
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Composite convex optimization with global and local inexact oracles
We introduce new global and local inexact oracle concepts for a wide class of convex functions in composite convex minimization. Such inexact oracles...
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Towards Computing High-Order p-Harmonic Descent Directions and Their Limits in Shape Optimization
We present an extension of an algorithm for the classical scalar p-Laplace Dirichlet problem to the vector-valued p-Laplacian with mixed boundary...
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Self-concordant inclusions: a unified framework for path-following generalized Newton-type algorithms
We study a class of monotone inclusions called “self-concordant inclusion” which covers three fundamental convex optimization formulations as special...
