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View article: Performance Analysis of Parameters of Classical Conjugate Gradient Methods Using Armijo Line Search
Performance Analysis of Parameters of Classical Conjugate Gradient Methods Using Armijo Line Search Open
View article: Iterative convergence in phase-field brittle fracture computations: exact line search is all you need
Iterative convergence in phase-field brittle fracture computations: exact line search is all you need Open
Variational phase-field models of brittle fracture pose a local constrained minimization problem of a non-convex energy functional. In the discrete setting, the problem is most often solved by alternate minimization, exploiting the separat…
View article: Iterative convergence in phase-field brittle fracture computations: exact line search is all you need
Iterative convergence in phase-field brittle fracture computations: exact line search is all you need Open
Variational phase-field models of brittle fracture pose a local constrained minimization problem of a non-convex energy functional. In the discrete setting, the problem is most often solved by alternate minimization, exploiting the separat…
View article: Enhanced kernel search algorithm for optimizing local search capability and its application to carbon fiber draft process
Enhanced kernel search algorithm for optimizing local search capability and its application to carbon fiber draft process Open
Kernel Search Optimization (KSO) is characterized by insufficient accuracy in local search, which makes it difficult to achieve local optimization. Therefore, this paper proposes a Large Local Search Kernel Search Optimization (LLSKSO) to …
View article: Algorithm parameters.
Algorithm parameters. Open
Kernel Search Optimization (KSO) is characterized by insufficient accuracy in local search, which makes it difficult to achieve local optimization. Therefore, this paper proposes a Large Local Search Kernel Search Optimization (LLSKSO) to…
View article: The set of Pareto solutions.
The set of Pareto solutions. Open
Kernel Search Optimization (KSO) is characterized by insufficient accuracy in local search, which makes it difficult to achieve local optimization. Therefore, this paper proposes a Large Local Search Kernel Search Optimization (LLSKSO) to…
View article: S1 Raw images.
S1 Raw images. Open
Kernel Search Optimization (KSO) is characterized by insufficient accuracy in local search, which makes it difficult to achieve local optimization. Therefore, this paper proposes a Large Local Search Kernel Search Optimization (LLSKSO) to…
View article: Benchmark test function results.
Benchmark test function results. Open
Kernel Search Optimization (KSO) is characterized by insufficient accuracy in local search, which makes it difficult to achieve local optimization. Therefore, this paper proposes a Large Local Search Kernel Search Optimization (LLSKSO) to…
View article: Benchmark test functions.
Benchmark test functions. Open
Kernel Search Optimization (KSO) is characterized by insufficient accuracy in local search, which makes it difficult to achieve local optimization. Therefore, this paper proposes a Large Local Search Kernel Search Optimization (LLSKSO) to…
View article: High-dimensional benchmark test functions.
High-dimensional benchmark test functions. Open
Kernel Search Optimization (KSO) is characterized by insufficient accuracy in local search, which makes it difficult to achieve local optimization. Therefore, this paper proposes a Large Local Search Kernel Search Optimization (LLSKSO) to…
View article: A globally convergent gradient method with momentum
A globally convergent gradient method with momentum Open
In this work, we consider smooth unconstrained optimization problems and we deal with the class of gradient methods with momentum, i.e., descent algorithms where the search direction is defined as a linear combination of the current gradie…
View article: Flow chart of carbon fiber production.
Flow chart of carbon fiber production. Open
Kernel Search Optimization (KSO) is characterized by insufficient accuracy in local search, which makes it difficult to achieve local optimization. Therefore, this paper proposes a Large Local Search Kernel Search Optimization (LLSKSO) to…
View article: Flowchart of LLSKSO.
Flowchart of LLSKSO. Open
Kernel Search Optimization (KSO) is characterized by insufficient accuracy in local search, which makes it difficult to achieve local optimization. Therefore, this paper proposes a Large Local Search Kernel Search Optimization (LLSKSO) to…
View article: Test function results.
Test function results. Open
Kernel Search Optimization (KSO) is characterized by insufficient accuracy in local search, which makes it difficult to achieve local optimization. Therefore, this paper proposes a Large Local Search Kernel Search Optimization (LLSKSO) to…
View article: Stochastic Adaptive Optimization with Unreliable Inputs: A Unified Framework for High-Probability Complexity Analysis
Stochastic Adaptive Optimization with Unreliable Inputs: A Unified Framework for High-Probability Complexity Analysis Open
We consider an unconstrained continuous optimization problem where, in each iteration, gradient estimates may be arbitrarily corrupted with a probability greater than 1/2. Additionally, function value estimates may exhibit heavy-tailed noi…
View article: Stochastic Adaptive Optimization with Unreliable Inputs: A Unified Framework for High-Probability Complexity Analysis
Stochastic Adaptive Optimization with Unreliable Inputs: A Unified Framework for High-Probability Complexity Analysis Open
We consider an unconstrained continuous optimization problem where, in each iteration, gradient estimates may be arbitrarily corrupted with a probability greater than 1/2. Additionally, function value estimates may exhibit heavy-tailed noi…
View article: Neighbor GRPO: Contrastive ODE Policy Optimization Aligns Flow Models
Neighbor GRPO: Contrastive ODE Policy Optimization Aligns Flow Models Open
Group Relative Policy Optimization (GRPO) has shown promise in aligning image and video generative models with human preferences. However, applying it to modern flow matching models is challenging because of its deterministic sampling para…
View article: Neighbor GRPO: Contrastive ODE Policy Optimization Aligns Flow Models
Neighbor GRPO: Contrastive ODE Policy Optimization Aligns Flow Models Open
Group Relative Policy Optimization (GRPO) has shown promise in aligning image and video generative models with human preferences. However, applying it to modern flow matching models is challenging because of its deterministic sampling para…
View article: The essential best and average rate of convergence of the exact line search gradient descent method
The essential best and average rate of convergence of the exact line search gradient descent method Open
It is very well known that when the exact line search gradient descent method is applied to a convex quadratic objective, the worst-case rate of convergence (ROC), among all seed vectors, deteriorates as the condition number of the Hessian…
View article: A Derivative-Free Method with the Symmetric Rank-One Update for Constrained Nonlinear Systems of Monotone Equations
A Derivative-Free Method with the Symmetric Rank-One Update for Constrained Nonlinear Systems of Monotone Equations Open
This paper presents a new derivative-free method with a symmetric rank-one (SR1) update for handling constrained nonlinear systems of monotone equations. Distinctively, the approach employs a revised SR1 update formula that leverages infor…
View article: Convergence Analysis of Tseng's Extragradient Method for Variational Inequalities with uniformly continuous Operators
Convergence Analysis of Tseng's Extragradient Method for Variational Inequalities with uniformly continuous Operators Open
In this paper, we consider variational inequality problems in real Hilbert spaces characterized by uniformly continuous and quasimonotone operators. To address them, we adopt Tseng's extragradient method equipped with a self-adaptive steps…
View article: An inexact semismooth Newton-Krylov method for semilinear elliptic optimal control problem
An inexact semismooth Newton-Krylov method for semilinear elliptic optimal control problem Open
An inexact semismooth Newton method has been proposed for solving semi-linear elliptic optimal control problems in this paper. This method incorporates the generalized minimal residual (GMRES) method, a type of Krylov subspace method, to s…
View article: An inexact semismooth Newton-Krylov method for semilinear elliptic optimal control problem
An inexact semismooth Newton-Krylov method for semilinear elliptic optimal control problem Open
An inexact semismooth Newton method has been proposed for solving semi-linear elliptic optimal control problems in this paper. This method incorporates the generalized minimal residual (GMRES) method, a type of Krylov subspace method, to s…
View article: Minimizing smooth Kurdyka-Łojasiewicz functions via generalized descent methods: Convergence rate and complexity
Minimizing smooth Kurdyka-Łojasiewicz functions via generalized descent methods: Convergence rate and complexity Open
This paper addresses the generalized descent algorithm (DEAL) for minimizing smooth functions, which is analyzed under the Kurdyka-Łojasiewicz (KL) inequality. In particular, the suggested algorithm guarantees a sufficient decrease by adap…
View article: Minimizing smooth Kurdyka-Łojasiewicz functions via generalized descent methods: Convergence rate and complexity
Minimizing smooth Kurdyka-Łojasiewicz functions via generalized descent methods: Convergence rate and complexity Open
This paper addresses the generalized descent algorithm (DEAL) for minimizing smooth functions, which is analyzed under the Kurdyka-Łojasiewicz (KL) inequality. In particular, the suggested algorithm guarantees a sufficient decrease by adap…
View article: Global iterative methods for sparse approximate inverses of symmetric positive-definite matrices
Global iterative methods for sparse approximate inverses of symmetric positive-definite matrices Open
The nonlinear (preconditioned) conjugate gradient N(P)CG method and the locally optimal (preconditioned) minimal residual LO(P)MR method, both of which are used for the iterative computation of sparse approximate inverses (SPAIs) of symmet…
View article: Global iterative methods for sparse approximate inverses of symmetric positive-definite matrices
Global iterative methods for sparse approximate inverses of symmetric positive-definite matrices Open
The nonlinear (preconditioned) conjugate gradient N(P)CG method and the locally optimal (preconditioned) minimal residual LO(P)MR method, both of which are used for the iterative computation of sparse approximate inverses (SPAIs) of symmet…
View article: Optimistic Online-to-Batch Conversions for Accelerated Convergence and Universality
Optimistic Online-to-Batch Conversions for Accelerated Convergence and Universality Open
In this work, we study offline convex optimization with smooth objectives, where the classical Nesterov's Accelerated Gradient (NAG) method achieves the optimal accelerated convergence. Extensive research has aimed to understand NAG from v…
View article: Optimistic Online-to-Batch Conversions for Accelerated Convergence and Universality
Optimistic Online-to-Batch Conversions for Accelerated Convergence and Universality Open
In this work, we study offline convex optimization with smooth objectives, where the classical Nesterov's Accelerated Gradient (NAG) method achieves the optimal accelerated convergence. Extensive research has aimed to understand NAG from v…
View article: Numerical results for Problem 8.
Numerical results for Problem 8. Open
In this paper, a hybrid conjugate gradient projection method for finding solutions of constrained nonlinear equations is proposed by integrating both hyperplane projection and hybrid techniques. The key features of this method are as foll…