Article
Operations Research & Management Science
Matteo Lapucci, Tommaso Levato, Marco Sciandrone
Summary: The manuscript discusses the problem of minimizing a smooth function with cardinality constraint. A modified penalty decomposition method is proposed to address the issue of computing the global minimum with respect to the original variables in the case of nonconvex objective function. Additionally, a derivative-free penalty decomposition algorithm for black-box optimization is presented, with convergence results and preliminary computational experiment results reported.
JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS
(2021)
Article
Automation & Control Systems
Yangfei Yuan, Weifeng Gao, Lingling Huang, Hong Li, Jin Xie
Summary: This article proposes a two-phase constraint-handling technique, called TPDE, for solving constrained optimization problems. In the exploration phase, an exterior penalty function method is used to push the population into the feasible region, while in the exploitation phase, an interior penalty function method is used to enhance the search ability. Experimental results show that TPDE is competitive with other popular algorithms on benchmark test suites.
IEEE TRANSACTIONS ON SYSTEMS MAN CYBERNETICS-SYSTEMS
(2023)
Article
Computer Science, Software Engineering
Hao Wang, Fan Zhang, Jiashan Wang, Yuyang Rong
Summary: This paper focuses on designing an inexact first-order algorithm for solving constrained nonlinear optimization problems, which reduces computational cost by controlling the inexactness of the subproblem solution. The proposed algorithm includes a penalty parameter updating strategy and has been proven to achieve global convergence.
OPTIMIZATION METHODS & SOFTWARE
(2022)
Article
Mathematics, Applied
Sebastian Blauth
Summary: In this paper, nonlinear conjugate gradient methods based on Steklov-Poincare-type metrics are proposed for solving shape optimization problems constrained by partial differential equations. The numerical comparison shows that these methods perform well in practice, making them an efficient and attractive addition to gradient-based shape optimization algorithms.
SIAM JOURNAL ON OPTIMIZATION
(2021)
Article
Computer Science, Artificial Intelligence
Tianwei Zhou, Pengcheng He, Ben Niu, Guanghui Yue, Hong Wang
Summary: In constrained multi-objective optimization problems, the c-DADSEA algorithm is proposed to balance convergence and diversity and find as many feasible solutions as possible. It introduces a convergence-driven archive and a diversity-driven archive, improves convergence by using an adaptive penalty function, enhances diversity with a dual-stage framework, and balances convergence and diversity with different benchmark rankings.
SWARM AND EVOLUTIONARY COMPUTATION
(2023)
Article
Mathematics, Applied
Albert S. Berahas, Frank E. Curtis, Daniel Robinson, Baoyu Zhou
Summary: Sequential quadratic optimization algorithms are proposed to solve smooth nonlinear optimization problems with equality constraints, especially focusing on cases where constraint functions are deterministic. The algorithm uses a stepsize selection scheme based on Lipschitz constants for deterministic settings.
SIAM JOURNAL ON OPTIMIZATION
(2021)
Article
Computer Science, Software Engineering
Alberto De Marchi, Xiaoxi Jia, Christian Kanzow, Patrick Mehlitz
Summary: This paper investigates finite-dimensional constrained structured optimization problems with composite objective functions and set-membership constraints. The problem class provides a modeling framework for various applications with an expressive yet simple language. The study focuses on stationarity and regularity concepts and proposes a flexible augmented Lagrangian scheme. The algorithm is theoretically characterized and its convergence results for fully nonconvex problems are derived. Additionally, a matrix-free implementation of the algorithm is described and numerically tested, showing the versatility of constrained composite programs as a modeling tool and the challenges arising in this problem class.
MATHEMATICAL PROGRAMMING
(2023)
Article
Automation & Control Systems
Michael R. Metel, Akiko Takeda
Summary: This paper focuses on stochastic proximal gradient methods for optimizing a smooth non-convex loss function with a non-smooth non-convex regularizer and convex constraints. The authors present the first non-asymptotic convergence bounds for this class of problem and compare their algorithms with the current state-of-the-art deterministic algorithm, finding superior convergence in a numerical experiment.
JOURNAL OF MACHINE LEARNING RESEARCH
(2021)
Article
Engineering, Civil
Dhirendra Sharma, Syeda Darakhshan Jabeen
Summary: This study presents a novel hybrid optimization approach inspired by interval analysis concepts and heuristics to effectively solve multiple engineering design problems. By combining the Split-Detect-Discard-Shrink technique with the Sophisticated ABC algorithm, the method optimizes computational efficiency and narrows down the search region for global or near-global solutions.
Article
Computer Science, Information Systems
Bing-Chuan Wang, Han-Xiong Li, Yun Feng, Wen-Jing Shen
Summary: The paper proposes an adaptive fuzzy penalty method to address the issue of tuning the penalty coefficient in constrained evolutionary optimization, adjusting the coefficient at both individual and population levels. By using differential evolution to design a search algorithm, the constrained optimization evolutionary algorithm AFPDE is proposed, showing competitiveness through experiments.
INFORMATION SCIENCES
(2021)
Article
Operations Research & Management Science
Qihang Lin, Runchao Ma, Yangyang Xu
Summary: This paper studies an inexact proximal-point penalty method for non-convex constrained optimization problems. The method approximately solves a sequence of subproblems to obtain the desired accuracy. The computational complexity is analyzed separately for convex and non-convex constraints, with complexity results established in terms of the number of proximal gradient steps.
COMPUTATIONAL OPTIMIZATION AND APPLICATIONS
(2022)
Article
Mathematics, Applied
Wei Liu, Xin Liu, Xiaojun Chen
Summary: An RP regularized minimization model is introduced for training autoencoders in two-layer neural networks, showing its effectiveness and robustness through comprehensive numerical experiments.
SIAM JOURNAL ON OPTIMIZATION
(2022)
Article
Automation & Control Systems
Changxin Liu, Yang Shi, Huiping Li, Wenli Du
Summary: In this article, decentralized convex constrained optimization problems in networks are studied. Two new decentralized dual averaging (DDA) algorithms are proposed, which achieve faster convergence compared to existing methods. The first algorithm uses a second-order dynamic average consensus protocol to estimate the global dual variable accurately. The second algorithm utilizes extrapolation technique and achieves fast convergence without relying on the spectrum of the mixing matrix.
IEEE TRANSACTIONS ON AUTOMATIC CONTROL
(2023)
Article
Computer Science, Artificial Intelligence
Ran Tao, Zeng Meng, Huanlin Zhou
Summary: The study focuses on the performance of Firefly Algorithm (FA) in engineering design problems and introduces an improved version with self-adaptive strategy (SAFA). By balancing the relationship between exploration and exploitation using self-adaptive strategies, the algorithm's performance is enhanced. When optimizing classical and CEC 2015 benchmark functions, SAFA achieves the best solutions in most cases.
APPLIED SOFT COMPUTING
(2021)
Article
Mathematics, Applied
Dominik Garmatter, Margherita Porcelli, Francesco Rinaldi, Martin Stoll
Summary: This article investigates penalization techniques as an alternative solution approach for optimal control problems with PDE and integer constraints. A novel improved penalty algorithm is proposed, incorporating a basin hopping strategy and an interior point method specialized for the problem class. Thorough numerical investigations demonstrate the versatility of the approach.
COMPUTERS & MATHEMATICS WITH APPLICATIONS
(2022)