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New Results on Superlinear Convergence of Classical Quasi-Newton Methods
We present a new theoretical analysis of local superlinear convergence of classical quasi-Newton methods from the convex Broyden class. As a result,...
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Computation of the Analytic Center of the Solution Set of the Linear Matrix Inequality Arising in Continuous- and Discrete-Time Passivity Analysis
In this paper formulas are derived for the analytic center of the solution set of linear matrix inequalities (LMIs) defining passive transfer...
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Solving Convex Min-Min Problems with Smoothness and Strong Convexity in One Group of Variables and Low Dimension in the Other
AbstractThe article deals with some approaches to solving convex problems of the min-min type with smoothness and strong convexity in only one of...
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Computational Optimal Transport
The optimal transport (OT) problem is a classical optimization problem having the form of linear programming. Machine learning applications put...
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Inexact proximal Newton methods for self-concordant functions
We analyze the proximal Newton method for minimizing a sum of a self-concordant function and a convex function with an inexpensive proximal operator....
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Complexity of a projected Newton-CG method for optimization with bounds
This paper describes a method for solving smooth nonconvex minimization problems subject to bound constraints with good worst-case complexity...
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Infeasible interior-point method for symmetric optimization using a positive-asymptotic barrier
We propose a new primal-dual infeasible interior-point method for symmetric optimization by using Euclidean Jordan algebras. Different kinds of...
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Finding global minima via kernel approximations
We consider the global minimization of smooth functions based solely on function evaluations. Algorithms that achieve the optimal number of function...
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Long-step path-following algorithm for solving symmetric programming problems with nonlinear objective functions
We developed a long-step path-following algorithm for a class of symmetric programming problems with nonlinear convex objective functions. The...
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Status determination by interior-point methods for convex optimization problems in domain-driven form
We study the geometry of convex optimization problems given in a Domain-Driven form and categorize possible statuses of these problems using duality...
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Newton Polytopes and Relative Entropy Optimization
Certifying function nonnegativity is a ubiquitous problem in computational mathematics, with especially notable applications in optimization. We...
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Mathematical optimization approach for facility layout on several rows
The facility layout problem is concerned with finding an arrangement of non-overlap** indivisible departments within a facility so as to minimize...
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A scaling-invariant algorithm for linear programming whose running time depends only on the constraint matrix
Following the breakthrough work of Tardos (Oper Res 34:250–256, 1986) in the bit-complexity model, Vavasis and Ye (Math Program 74(1):79–120, 1996)...
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Nonlinear Rescaling: Theory and Methods
The first result on Nonlinear Rescaling (NR) theory and methods were obtained in the early 1980s. The purpose was finding an alternative for SUMT...
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Subgradient ellipsoid method for nonsmooth convex problems
In this paper, we present a new ellipsoid-type algorithm for solving nonsmooth problems with convex structure. Examples of such problems include...
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Kernel density estimation based distributionally robust mean-CVaR portfolio optimization
In this paper, by using weighted kernel density estimation (KDE) to approximate the continuous probability density function (PDF) of the portfolio...
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Matrix monotonicity and self-concordance: how to handle quantum entropy in optimization problems
Let g be a continuously differentiable function whose derivative is matrix monotone on the positive semi-axis. Such a function induces a function
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Optimization in Relative Scale
In many applications, it is difficult to relate the number of iterations in an optimization scheme with the desired accuracy of the solution since...
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Self-concordance is NP-hard
We show that deciding whether a convex function is self-concordant is in general an intractable problem.