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Optimization in complex spaces with the mixed Newton method
We propose a second-order method for unconditional minimization of functions f ( z ) of complex arguments. We call it the mixed Newton method due to the...
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The Newton Method
In the panoply of the optimization methods and in general, for solving problems that have an algebraic mathematical model, the Newton method has a...
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On Local Behavior of Newton-Type Methods Near Critical Solutions of Constrained Equations
For constrained equations with nonisolated solutions and a certain family of Newton-type methods, it was previously shown that if the equation...
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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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Combined Newton-Gradient Method for Constrained Root-Finding in Chemical Reaction Networks
In this work, we present a fast, globally convergent, iterative algorithm for computing the asymptotically stable states of nonlinear large-scale...
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A Dual Semismooth Newton Based Augmented Lagrangian Method for Large-Scale Linearly Constrained Sparse Group Square-Root Lasso Problems
Square-root Lasso problems have already be shown to be robust regression problems. Furthermore, square-root regression problems with structured...
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Behavior of Newton-Type Methods Near Critical Solutions of Nonlinear Equations with Semismooth Derivatives
Having in mind singular solutions of smooth reformulations of complementarity problems, arising unavoidably when the solution in question violates...
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On a primal-dual Newton proximal method for convex quadratic programs
This paper introduces QPDO, a primal-dual method for convex quadratic programs which builds upon and weaves together the proximal point algorithm and...
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A semismooth Newton based dual proximal point algorithm for maximum eigenvalue problem
The maximum eigenvalue problem is to minimize the maximum eigenvalue function over an affine subspace in a symmetric matrix space, which has many...
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A Semismooth Newton-based Augmented Lagrangian Algorithm for Density Matrix Least Squares Problems
The density matrix least squares problem arises from the quantum state tomography problem in experimental physics and has many applications in signal...
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Regularization of limited memory quasi-Newton methods for large-scale nonconvex minimization
This paper deals with regularized Newton methods, a flexible class of unconstrained optimization algorithms that is competitive with line search and...
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Non-asymptotic superlinear convergence of standard quasi-Newton methods
In this paper, we study and prove the non-asymptotic superlinear convergence rate of the Broyden class of quasi-Newton algorithms which includes the...
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Hessian averaging in stochastic Newton methods achieves superlinear convergence
We consider minimizing a smooth and strongly convex objective function using a stochastic Newton method. At each iteration, the algorithm is given an...
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Mass, center of mass and isoperimetry in asymptotically flat 3-manifolds
We revisit the interplay between the mass, the center of mass and the large scale behavior of certain isoperimetric quotients in the setting of...
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Convergence of Inertial Dynamics Driven by Sums of Potential and Nonpotential Operators with Implicit Newton-Like Dam**
We analyze the convergence properties when the time t tends to infinity of the trajectories generated by damped inertial dynamics which are driven by...
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On the asymptotic rate of convergence of Stochastic Newton algorithms and their Weighted Averaged versions
Most machine learning methods can be regarded as the minimization of an unavailable risk function. To optimize the latter, with samples provided in a...
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A Symbolic-Numeric Validation Algorithm for Linear ODEs with Newton–Picard Method
A symbolic-numeric validation algorithm is developed to compute rigorous and tight uniform error bounds for polynomial approximate solutions to...
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Stochastic Gauss–Newton Algorithms for Online PCA
In this paper, we propose a stochastic Gauss–Newton (SGN) algorithm to study the online principal component analysis (OPCA) problem, which is...
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Proximal Gradient/Semismooth Newton Methods for Projection onto a Polyhedron via the Duality-Gap-Active-Set Strategy
The polyhedral projection problem arises in various applications. To efficiently solve the dual problem, one of the crucial issues is to safely...
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The Newton product of polynomial projectors. Part 2: approximation properties
We prove that the Newton product of efficient polynomial projectors is still efficient. Various polynomial approximation theorems are established...