Efficient Riemannian Inexact Augmented Lagrangian Method for Nonsmooth Composite Optimization on Manifolds
The proposed Riemannian inexact augmented Lagrangian (RiAL) method can find an ε-stationary point of a class of Riemannian nonsmooth composite problems with O(ε^-3) first-order oracle calls, achieving the best known oracle complexity.
일반화된 로그-행렬식 반정부 프로그래밍을 위한 이중 스펙트럼 투영 경사 방법
일반화된 로그-행렬식 반정부 프로그래밍 문제를 효율적으로 해결하기 위해 이중 스펙트럼 투영 경사 방법을 제안하고, 이 방법의 수렴성을 분석하였다.
一般化された対数行列式半正定値計画問題のための双対スペクトル射影勾配法
本論文では、対数行列式半正定値計画問題の一般化された形式を扱い、その双対問題を効率的に解くための双対スペクトル射影勾配法を提案する。提案手法は、様々な構造を持つガウス グラフィカルモデルに適用可能であり、最適値への収束が保証される。
Efficient Dual Spectral Projected Gradient Method for Generalized Log-Determinant Semidefinite Programming
The authors propose an efficient dual spectral projected gradient (DSPG) method for solving a generalized log-determinant semidefinite programming (SDP) problem, which covers a wide range of structures in Gaussian graphical models. The method extends the previous DSPG approach to handle the generalized problem structure and provides convergence guarantees.
Efficient Projected Newton Framework for Computing Exact Optimal Experimental Designs
The authors propose a novel projected Newton framework, combined with a vertex exchange method, to efficiently solve the continuous relaxations within a branch-and-bound algorithm for computing exact optimal experimental designs.
Optimizing Swine Diets Using Multi-objective Regionalized Bayesian Optimization
Developing cost-effective swine diet formulations that balance minimum nutritional requirements using multi-objective regionalized Bayesian optimization.
Efficient Optimization on the Random Generalized Stiefel Manifold without Retraction
The authors propose a cheap stochastic iterative method that solves the optimization problem on the random generalized Stiefel manifold without requiring expensive eigenvalue decompositions or matrix inversions. The method has lower per-iteration cost, requires only matrix multiplications, and has the same convergence rates as its Riemannian counterparts.
An Adaptive Linearized Alternating Direction Multiplier Method for Solving Convex Optimization Problems
The proposed adaptive linearized alternating direction multiplier method improves the convergence rate of the algorithm by dynamically selecting the regular term coefficients based on the current iteration point, without compromising the convergence.
Robustness Analysis of Perturbed Gradient Flows for the Linear Quadratic Regulator Problem
The perturbed gradient flow for the linear quadratic regulator (LQR) problem is shown to be small-disturbance input-to-state stable (ISS) under suitable conditions on the objective function.
시간 변화하는 선형 등식 및 부등식 제약 조건이 있는 온라인 최적화 문제에 대한 제어 이론적 접근법
제어 이론을 활용하여 시간 변화하는 선형 등식 및 부등식 제약 조건이 있는 온라인 최적화 문제를 해결하는 새로운 알고리즘을 제안한다. 등식 제약만 있는 경우 강건 제어를 사용하여 최적 궤적에 점근적으로 수렴하는 온라인 알고리즘을 설계하였다. 부등식 제약이 있는 경우에는 이를 처리하기 위해 anti-windup 기법을 활용하였다.
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