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Extrapolated Smoothing Descent Algorithm for Constrained Nonconvex and Nonsmooth Composite Problems
In this paper, the authors propose a novel smoothing descent type algorithm with extrapolation for solving a class of constrained nonsmooth and...
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Convergence of Dirichlet Energy Minimization for Spherical Conformal Parameterizations
In this paper, we first derive a theoretical basis for spherical conformal parameterizations between a simply connected closed surface
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Binary Quantized Network Training With Sharpness-Aware Minimization
The quantized neural network is a common way to improve inference and memory efficiency for deep learning methods. However, it is challenging to...
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Hybrid limited memory gradient projection methods for box-constrained optimization problems
Gradient projection methods represent effective tools for solving large-scale constrained optimization problems thanks to their simple implementation...
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Convergence Rate of Gradient-Concordant Methods for Smooth Unconstrained Optimization
The article discusses the class of gradient-concordant numerical methods for smooth unconstrained minimization where the descent direction is...
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Domain Decomposition for Non-smooth (in Particular TV) Minimization
Domain decomposition is one of the most efficient techniques to derive efficient methods for large-scale problems. In this chapter such decomposition...
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A neurodynamic approach for joint chance constrained rectangular geometric optimization
This paper considers a nonconvex geometric optimization problem with two-sided joint probabilistic constraints, namely rectangular constraints. We...
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A dynamical neural network approach for distributionally robust chance-constrained Markov decision process
In this paper, we study the distributionally robust joint chance-constrained Markov decision process. Utilizing the logarithmic transformation...
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An alternating structure-adapted Bregman proximal gradient descent algorithm for constrained nonconvex nonsmooth optimization problems and its inertial variant
We consider the nonconvex nonsmooth minimization problem over abstract sets, whose objective function is the sum of a proper lower semicontinuous...
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Inexact generalized ADMM with relative error criteria for linearly constrained convex optimization problems
The alternating direction method of multipliers (ADMM) and its variants are widely used in solving practical problems. However, the efficiency of...
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Nonlinear conjugate gradient for smooth convex functions
The method of nonlinear conjugate gradients (NCG) is widely used in practice for unconstrained optimization, but it satisfies weak complexity bounds...
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Numerical Solution for Sparse PDE Constrained Optimization
In this chapter, elliptic PDE-constrained optimal control problems with L1-control cost (L1-EOCP) are considered. Motivated by the success of the...
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A stochastic first-order trust-region method with inexact restoration for finite-sum minimization
We propose a stochastic first-order trust-region method with inexact function and gradient evaluations for solving finite-sum minimization problems....
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Convergence analysis of generalized ADMM with majorization for linearly constrained composite convex optimization
The generalized alternating direction method of multipliers (ADMM) of **ao et al. (Math Prog Comput 10:533–555, 2018) aims at the two-block linearly...
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Convergence of derivative-free nonmonotone Direct Search Methods for unconstrained and box-constrained mixed-integer optimization
This paper presents a class of nonmonotone Direct Search Methods that converge to stationary points of unconstrained and boxed constrained...
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Second order semi-smooth Proximal Newton methods in Hilbert spaces
We develop a globalized Proximal Newton method for composite and possibly non-convex minimization problems in Hilbert spaces. Additionally, we impose...
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DC semidefinite programming and cone constrained DC optimization II: local search methods
The second part of our study is devoted to a detailed convergence analysis of two extensions of the well-known DCA method for solving DC (Difference...
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Numerical Approaches for Constrained and Unconstrained, Static Optimization on the Special Euclidean Group SE(3)
In this paper, rigid body static optimization is investigated on the Riemannian manifold of rigid body motion groups. This manifold, which is also a...
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A solution method for mixed-variable constrained blackbox optimization problems
Many real-world application problems encountered in industry have no analytical formulation, that is they are blackbox optimization problems, and...
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Zero-Order Stochastic Conditional Gradient Sliding Method for Non-smooth Convex Optimization
The conditional gradient idea proposed by Marguerite Frank and Philip Wolfe in 1956 was so well received by the community that new algorithms (also...