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Journal articles on the topic 'Convex and nonconvex optimisation'

Author: Grafiati

Published: 11 December 2022

Last updated: 31 July 2025

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1

Martínez-legaz, J. E., and A. Seeger. "A formula on the approximate subdifferential of the difference of convex functions." Bulletin of the Australian Mathematical Society 45, no. 1 (1992): 37–41. http://dx.doi.org/10.1017/s0004972700036984.

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We give a formula on the ε−subdifferential of the difference of two convex functions. As a by-product of this formula, one recovers a recent result of Hiriart-Urruty, namely, a necessary and sufficient condition for global optimality in nonconvex optimisation.

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2

Gustafson, Sven-Åke. "Investigating semi-infinite programs using penalty functions and Lagrangian methods." Journal of the Australian Mathematical Society. Series B. Applied Mathematics 28, no. 2 (1986): 158–69. http://dx.doi.org/10.1017/s0334270000005270.

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AbstractIn this paper the relations between semi-infinite programs and optimisation problems with finitely many variables and constraints are reviewed. Two classes of convex semi-infinite programs are defined, one based on the fact that a convex set may be represented as the intersection of closed halfspaces, while the other class is defined using the representation of the elements of a convex set as convex combinations of points and directions. Extension to nonconvex problems is given. A common technique of solving a semi-infinite program computationally is to derive necessary conditions for

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3

Thi, Hoai An Le, Hoai Minh Le, and Tao Pham Dinh. "Fuzzy clustering based on nonconvex optimisation approaches using difference of convex (DC) functions algorithms." Advances in Data Analysis and Classification 1, no. 2 (2007): 85–104. http://dx.doi.org/10.1007/s11634-007-0011-2.

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4

Lanza, A., S. Morigi, I. Selesnick, and F. Sgallari. "Nonconvex nonsmooth optimization via convex–nonconvex majorization–minimization." Numerische Mathematik 136, no. 2 (2016): 343–81. http://dx.doi.org/10.1007/s00211-016-0842-x.

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5

Penot, J. P. "Conditioning convex and nonconvex problems." Journal of Optimization Theory and Applications 90, no. 3 (1996): 535–54. http://dx.doi.org/10.1007/bf02189795.

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6

Smith, E. "Global Optimisation of Nonconvex MINLPs." Computers & Chemical Engineering 21, no. 1-2 (1997): S791—S796. http://dx.doi.org/10.1016/s0098-1354(97)00146-4.

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7

Smith, Edward M. B., and Constantinos C. Pantelides. "Global optimisation of nonconvex MINLPs." Computers & Chemical Engineering 21 (May 1997): S791—S796. http://dx.doi.org/10.1016/s0098-1354(97)87599-0.

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8

Vilchez Membrilla, José Antonio, Víctor Salas Moreno, Soledad Moreno-Pulido, Alberto Sánchez-Alzola, Clemente Cobos Sánchez, and Francisco Javier García-Pacheco. "Minimization over Nonconvex Sets." Symmetry 16, no. 7 (2024): 809. http://dx.doi.org/10.3390/sym16070809.

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Minimum norm problems consist of finding the distance of a closed subset of a normed space to the origin. Usually, the given closed subset is also asked to be convex, thus resulting in a convex minimum norm problem. There are plenty of techniques and algorithms to compute the distance of a closed convex set to the origin, which mostly exist in the Hilbert space setting. In this manuscript, we consider nonconvex minimum norm problems that arise from Bioengineering and reformulate them in such a way that the solution to their reformulation is already known. In particular, we tackle the problem o

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9

Eichfelder, Gabriele, and Patrick Groetzner. "A note on completely positive relaxations of quadratic problems in a multiobjective framework." Journal of Global Optimization 82, no. 3 (2021): 615–26. http://dx.doi.org/10.1007/s10898-021-01091-2.

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AbstractIn a single-objective setting, nonconvex quadratic problems can equivalently be reformulated as convex problems over the cone of completely positive matrices. In small dimensions this cone equals the cone of matrices which are entrywise nonnegative and positive semidefinite, so the convex reformulation can be solved via SDP solvers. Considering multiobjective nonconvex quadratic problems, naturally the question arises, whether the advantage of convex reformulations extends to the multicriteria framework. In this note, we show that this approach only finds the supported nondominated poi

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10

Keller, André A. "Convex underestimating relaxation techniques for nonconvex polynomial programming problems: computational overview." Journal of the Mechanical Behavior of Materials 24, no. 3-4 (2015): 129–43. http://dx.doi.org/10.1515/jmbm-2015-0015.

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AbstractThis paper introduces constructing convex-relaxed programs for nonconvex optimization problems. Branch-and-bound algorithms are convex-relaxation-based techniques. The convex envelopes are important, as they represent the uniformly best convex underestimators for nonconvex polynomials over some region. The reformulation-linearization technique (RLT) generates linear programming (LP) relaxations of a quadratic problem. RLT operates in two steps: a reformulation step and a linearization (or convexification) step. In the reformulation phase, the constraint and bound inequalities are repla

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11

Xu, Wenbo, Muhammad Imran, Faisal Yasin, Nazia Jahangir, and Qunli Xia. "Fractional Versions of Hermite-Hadamard, Fejér, and Schur Type Inequalities for Strongly Nonconvex Functions." Journal of Function Spaces 2022 (July 18, 2022): 1–8. http://dx.doi.org/10.1155/2022/7361558.

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In modern world, most of the optimization problems are nonconvex which are neither convex nor concave. The objective of this research is to study a class of nonconvex functions, namely, strongly nonconvex functions. We establish inequalities of Hermite-Hadamard and Fejér type for strongly nonconvex functions in generalized sense. Moreover, we establish some fractional integral inequalities for strongly nonconvex functions in generalized sense in the setting of Riemann-Liouville integral operators.

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12

Wang, Xiaoliang, Liping Pang, Qi Wu, and Mingkun Zhang. "An Adaptive Proximal Bundle Method with Inexact Oracles for a Class of Nonconvex and Nonsmooth Composite Optimization." Mathematics 9, no. 8 (2021): 874. http://dx.doi.org/10.3390/math9080874.

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In this paper, an adaptive proximal bundle method is proposed for a class of nonconvex and nonsmooth composite problems with inexact information. The composite problems are the sum of a finite convex function with inexact information and a nonconvex function. For the nonconvex function, we design the convexification technique and ensure the linearization errors of its augment function to be nonnegative. Then, the sum of the convex function and the augment function is regarded as an approximate function to the primal problem. For the approximate function, we adopt a disaggregate strategy and re

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13

Knill, Oliver. "On Nonconvex Caustics of Convex Billiards." Elemente der Mathematik 53, no. 3 (1998): 89–106. http://dx.doi.org/10.1007/s000170050038.

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14

Mehmet Zeki SARIKAYA, Hakan Bozkurt, and Mehmet Eyüp KIRIS. "On Hermite-Hadamard type integral inequalities for functions whose second derivative are nonconvex." Malaya Journal of Matematik 2, no. 03 (2014): 293–300. http://dx.doi.org/10.26637/mjm203/016.

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In this paper, we extend some estimates of the right hand side of a Hermite- Hadamard type inequality for nonconvex functions whose second derivatives absolute values are $\varphi$-convex, $\log -\varphi$-convex, and quasi- $\varphi$ convex.

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15

Cong, Chang, and Peibiao Zhao. "Non-Cash Risk Measure on Nonconvex Sets." Mathematics 6, no. 10 (2018): 186. http://dx.doi.org/10.3390/math6100186.

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Monetary risk measures are interpreted as the smallest amount of external cash that must be added to a financial position to make the position acceptable. In this paper, A new concept: non-cash risk measure is proposed and this measure provides an approach to transform the unacceptable positions into the acceptable positions in a nonconvex set. Non-cash risk measure uses not only cash but also other kinds of assets to adjust the position. This risk measure is nonconvex due to the use of optimization problem in L 1 norm. A convex extension of the nonconvex risk measure is derived and the relati

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16

Hong, Tao, and Geng-xin Zhang. "Power Allocation for Reducing PAPR of Artificial-Noise-Aided Secure Communication System." Mobile Information Systems 2020 (July 18, 2020): 1–15. http://dx.doi.org/10.1155/2020/6203079.

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The research of improving the secrecy capacity (SC) of wireless communication system using artificial noise (AN) is one of the classic models in the field of physical layer security communication. In this paper, we consider the peak-to-average power ratio (PAPR) problem in this AN-aided model. A power allocation algorithm for AN subspaces is proposed to solve the nonconvex optimization problem of PAPR. This algorithm utilizes a series of convex optimization problems to relax the nonconvex optimization problem in a convex way based on fractional programming, difference of convex (DC) functions

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17

Li, Jueyou, Chuanye Gu, Zhiyou Wu, and Changzhi Wu. "Distributed Optimization Methods for Nonconvex Problems with Inequality Constraints over Time-Varying Networks." Complexity 2017 (2017): 1–10. http://dx.doi.org/10.1155/2017/3610283.

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Network-structured optimization problems are found widely in engineering applications. In this paper, we investigate a nonconvex distributed optimization problem with inequality constraints associated with a time-varying multiagent network, in which each agent is allowed to locally access its own cost function and collaboratively minimize a sum of nonconvex cost functions for all the agents in the network. Based on successive convex approximation techniques, we first approximate locally the nonconvex problem by a sequence of strongly convex constrained subproblems. In order to realize distribu

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18

Bounkhel, Messaoud. "Generalized $ (f, \lambda) $-projection operator on closed nonconvex sets and its applications in reflexive smooth Banach spaces." AIMS Mathematics 8, no. 12 (2023): 29555–68. http://dx.doi.org/10.3934/math.20231513.

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<abstract><p>In this paper, we expanded from the convex case to the nonconvex case in the setting of reflexive smooth Banach spaces, the concept of the $ f $-generalized projection $ \pi^{f}_S:X^*\to S $ initially introduced for convex sets and convex functions in <sup>[<xref ref-type="bibr" rid="b19">19</xref>,<xref ref-type="bibr" rid="b20">20</xref>]</sup>. Indeed, we defined the $ (f, \lambda) $-generalized projection operator $ \pi^{f, \lambda}_S:X^*\to S $ from $ X^* $ onto a nonempty closed set $ S $. We proved many properties of $ \pi^{f,

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19

Ушаков, Владимир Николаевич, Vladimir Ushakov, Александр Анатольевич Ершов, and Alexandr Ershov. "On the guaranteed estimates of the area of convex subsets of compacts on a plane." Mathematical Game Theory and Applications 12, no. 4 (2020): 112–26. http://dx.doi.org/10.17076/mgta_2020_4_28.

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The paper considers the problem of constructing a convex subset of the largest area in a nonconvex compact on the plane, as well as the problem of constructing a convex subset from which the Hausdorff deviation of the compact is minimal. Since, in the general case, the exact solution of these problems is impossible, the geometric difference between the convex hull of a compact and a circle of a certain radius is proposed as an acceptable replacement for the exact solution. A lower bound for the area of this geometric difference and an upper bound for the Hausdorff deviation from it of a given

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20

Xu, Yi, and Lili Han. "Quadratic Program on a Structured Nonconvex Set." Mathematical Problems in Engineering 2020 (March 12, 2020): 1–6. http://dx.doi.org/10.1155/2020/4318186.

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In this paper, we focus on a special nonconvex quadratic program whose feasible set is a structured nonconvex set. To find an effective method to solve this nonconvex program, we construct a bilevel program, where the low-level program is a convex program while the upper-level program is a small-scale nonconvex program. Utilizing some properties of the bilevel program, we propose a new algorithm to solve this special quadratic program. Finally, numerical results show that our new method is effective and efficient.

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21

Chrétien, Stéphane, and Pascal Bondon. "Projection Methods for Uniformly Convex Expandable Sets." Mathematics 8, no. 7 (2020): 1108. http://dx.doi.org/10.3390/math8071108.

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Many problems in medical image reconstruction and machine learning can be formulated as nonconvex set theoretic feasibility problems. Among efficient methods that can be put to work in practice, successive projection algorithms have received a lot of attention in the case of convex constraint sets. In the present work, we provide a theoretical study of a general projection method in the case where the constraint sets are nonconvex and satisfy some other structural properties. We apply our algorithm to image recovery in magnetic resonance imaging (MRI) and to a signal denoising in the spirit of

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22

SINGH, I. V., B. K. MISHRA, and MOHIT PANT. "AN EFFICIENT PARTIAL DOMAIN ENRICHED ELEMENT-FREE GALERKIN METHOD CRITERION FOR CRACKS IN NONCONVEX DOMAINS." International Journal of Modeling, Simulation, and Scientific Computing 02, no. 03 (2011): 317–36. http://dx.doi.org/10.1142/s1793962311000475.

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In the present work, an efficient partial domain, intrinsic, enriched element-free Galerkin criterion has been extended to simulate the cracks lying in nonconvex domains. According to this criterion, only a part of the domain near the crack tip has been enriched. A linear ramp function has been used to avoid the sudden truncation of the enrichment effect. Some cases of cracks lying in convex as well as in nonconvex domains have been solved by both full and partial domain enrichment criteria under plane stress conditions. For the cracks lying in convex domain, the results obtained by full domai

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23

Yang, Yixin, Zhaohui Du, Yong Wang, Xijing Guo, Long Yang, and Jianbo Zhou. "Convex compressive beamforming with nonconvex sparse regularization." Journal of the Acoustical Society of America 149, no. 2 (2021): 1125–37. http://dx.doi.org/10.1121/10.0003373.

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24

Anza Hafsa, Omar, and Jean-Philippe Mandallena. "Homogenization of nonconvex integrals with convex growth." Journal de Mathématiques Pures et Appliquées 96, no. 2 (2011): 167–89. http://dx.doi.org/10.1016/j.matpur.2011.03.003.

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25

Dutta, Joydeep. "On convex vector optimisation." Bulletin of the Australian Mathematical Society 61, no. 1 (2000): 85–88. http://dx.doi.org/10.1017/s0004972700022036.

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In this article we present a simple method to deduce necessary conditions for weak minimisation of a convex vector program in a Banach space. Our main tool here will be the generalised Jabcobian of Ralph.

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26

Bounkhel, M., and Dj Bounekhel. "Iterative Schemes for Nonconvex Quasi-Variational Problems with V-Prox-Regular Data in Banach Spaces." Journal of Function Spaces 2017 (2017): 1–11. http://dx.doi.org/10.1155/2017/8708065.

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In this paper, we propose an extension of quasi-equilibrium problems from the convex case to the nonconvex case and from Hilbert spaces to Banach spaces. The proposed problem is called quasi-variational problem. We study the convergence of some algorithms to solutions of the proposed nonconvex problems in Banach spaces.

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27

Chernyaev, Yu A. "Conditional Gradient Method for Optimization Problems with a Constraint in the Form of the Intersection of a Convex Smooth Surface and a Convex Compact Set." Журнал вычислительной математики и математической физики 63, no. 7 (2023): 1100–1107. http://dx.doi.org/10.31857/s0044466923070049.

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The conditional gradient method is generalized to nonconvex sets of constraints representing the set-theoretic intersection of a convex smooth surface and a convex compact set. Necessary optimality conditions are studied, and the convergence of the method is analyzed.

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28

Yuan, Ganzhao. "Coordinate Descent Methods for DC Minimization: Optimality Conditions and Global Convergence." Proceedings of the AAAI Conference on Artificial Intelligence 37, no. 9 (2023): 11034–42. http://dx.doi.org/10.1609/aaai.v37i9.26307.

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Difference-of-Convex (DC) minimization, referring to the problem of minimizing the difference of two convex functions, has been found rich applications in statistical learning and studied extensively for decades. However, existing methods are primarily based on multi-stage convex relaxation, only leading to weak optimality of critical points. This paper proposes a coordinate descent method for minimizing a class of DC functions based on sequential nonconvex approximation. Our approach iteratively solves a nonconvex one-dimensional subproblem globally, and it is guaranteed to converge to a coor

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29

Contreras, José N. "Exploring Nonconvex, Crossed, and Degenerate Polygons." Mathematics Teacher 98, no. 2 (2004): 80–86. http://dx.doi.org/10.5951/mt.98.2.0080.

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How interactive software can be used to extend mathematical conjectures and theorems to non–convex, crossed, and degenerate polygons. The author demonstrates investigating Napoleon's Theorem with Geometer's Sketchpad.

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30

Ghafari, N., and H. Mohebi. "Optimality conditions for nonconvex problems over nearly convex feasible sets." Arabian Journal of Mathematics 10, no. 2 (2021): 395–408. http://dx.doi.org/10.1007/s40065-021-00315-3.

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AbstractIn this paper, we study the optimization problem (P) of minimizing a convex function over a constraint set with nonconvex constraint functions. We do this by given new characterizations of Robinson’s constraint qualification, which reduces to the combination of generalized Slater’s condition and generalized sharpened nondegeneracy condition for nonconvex programming problems with nearly convex feasible sets at a reference point. Next, using a version of the strong CHIP, we present a constraint qualification which is necessary for optimality of the problem (P). Finally, using new charac

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31

Li, Zichong, and Yangyang Xu. "Augmented Lagrangian–Based First-Order Methods for Convex-Constrained Programs with Weakly Convex Objective." INFORMS Journal on Optimization 3, no. 4 (2021): 373–97. http://dx.doi.org/10.1287/ijoo.2021.0052.

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First-order methods (FOMs) have been widely used for solving large-scale problems. A majority of existing works focus on problems without constraint or with simple constraints. Several recent works have studied FOMs for problems with complicated functional constraints. In this paper, we design a novel augmented Lagrangian (AL)–based FOM for solving problems with nonconvex objective and convex constraint functions. The new method follows the framework of the proximal point (PP) method. On approximately solving PP subproblems, it mixes the usage of the inexact AL method (iALM) and the quadratic

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32

Luo, Zhijun, Zhibin Zhu, and Benxin Zhang. "A LogTVSCAD Nonconvex Regularization Model for Image Deblurring in the Presence of Impulse Noise." Discrete Dynamics in Nature and Society 2021 (October 26, 2021): 1–19. http://dx.doi.org/10.1155/2021/3289477.

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This paper proposes a nonconvex model (called LogTVSCAD) for deblurring images with impulsive noises, using the log-function penalty as the regularizer and adopting the smoothly clipped absolute deviation (SCAD) function as the data-fitting term. The proposed nonconvex model can effectively overcome the poor performance of the classical TVL1 model for high-level impulsive noise. A difference of convex functions algorithm (DCA) is proposed to solve the nonconvex model. For the model subproblem, we consider the alternating direction method of multipliers (ADMM) algorithm to solve it. The global

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33

Bounkhel, Messaoud. "Existence Results for First and Second Order Nonconvex Sweeping Processes with Perturbations and with Delay: Fixed Point Approach." gmj 13, no. 2 (2006): 239–49. http://dx.doi.org/10.1515/gmj.2006.239.

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Abstract We are interested in existence results for nonconvex functional differential inclusions. First, we prove an existence result, in separable Hilbert spaces, for first order nonconvex sweeping processes with perturbation and with delay. Then, by using this result and a fixed point theorem we prove an existence result for second order nonconvex sweeping processes with perturbation and with delay of the form 𝑢˙ (𝑡) ∈ 𝐶(𝑢(𝑡)), 𝑢¨(𝑡) ∈ –𝑁𝑃(𝐶(𝑢(𝑡)); 𝑢˙(𝑡)) + 𝐹(𝑡, 𝑢˙𝑡) when 𝐶 is a nonconvex bounded Lipschitz set-valued mapping and 𝐹 is a set-valued mapping with convex compact values taking the

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34

Liu, Yang, and Yazheng Dang. "Convergence Analysis of Multiblock Inertial ADMM for Nonconvex Consensus Problem." Journal of Mathematics 2023 (March 28, 2023): 1–12. http://dx.doi.org/10.1155/2023/4316267.

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The alternating direction method of multipliers (ADMM) is one of the most powerful and successful methods for solving various nonconvex consensus problem. The convergence of the conventional ADMM (i.e., 2-block) for convex objective functions has been stated for a long time. As an accelerated technique, the inertial effect was used by many authors to solve 2-block convex optimization problem. This paper combines the ADMM and the inertial effect to construct an inertial alternating direction method of multipliers (IADMM) to solve the multiblock nonconvex consensus problem and shows the converge

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35

Dutta, Aritra, Filip Hanzely, and Peter Richtàrik. "A Nonconvex Projection Method for Robust PCA." Proceedings of the AAAI Conference on Artificial Intelligence 33 (July 17, 2019): 1468–76. http://dx.doi.org/10.1609/aaai.v33i01.33011468.

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Robust principal component analysis (RPCA) is a well-studied problem whose goal is to decompose a matrix into the sum of low-rank and sparse components. In this paper, we propose a nonconvex feasibility reformulation of RPCA problem and apply an alternating projection method to solve it. To the best of our knowledge, this is the first paper proposing a method that solves RPCA problem without considering any objective function, convex relaxation, or surrogate convex constraints. We demonstrate through extensive numerical experiments on a variety of applications, including shadow removal, backgr

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36

Grad, Sorin-Mihai, and Felipe Lara. "Solving Mixed Variational Inequalities Beyond Convexity." Journal of Optimization Theory and Applications 190, no. 2 (2021): 565–80. http://dx.doi.org/10.1007/s10957-021-01860-9.

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AbstractWe show that Malitsky’s recent Golden Ratio Algorithm for solving convex mixed variational inequalities can be employed in a certain nonconvex framework as well, making it probably the first iterative method in the literature for solving generalized convex mixed variational inequalities, and illustrate this result by numerical experiments.

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Liu, Xinfu, and Ping Lu. "Solving Nonconvex Optimal Control Problems by Convex Optimization." Journal of Guidance, Control, and Dynamics 37, no. 3 (2014): 750–65. http://dx.doi.org/10.2514/1.62110.

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38

Papadakis, Nicolas, Romain Yildizoğlu, Jean-François Aujol, and Vicent Caselles. "High-Dimension Multilabel Problems: Convex or Nonconvex Relaxation?" SIAM Journal on Imaging Sciences 6, no. 4 (2013): 2603–39. http://dx.doi.org/10.1137/120900307.

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39

Shen, Xinyue, and Yuantao Gu. "Nonconvex Sparse Logistic Regression With Weakly Convex Regularization." IEEE Transactions on Signal Processing 66, no. 12 (2018): 3199–211. http://dx.doi.org/10.1109/tsp.2018.2824289.

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Gabeleh, Moosa, and Olivier Olela Otafudu. "Nonconvex proximal normal structure in convex metric spaces." Banach Journal of Mathematical Analysis 10, no. 2 (2016): 400–414. http://dx.doi.org/10.1215/17358787-3495759.

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41

Fukuyama, Hirofumi, and Rashed Khanjani Shiraz. "Cost-effectiveness measures on convex and nonconvex technologies." European Journal of Operational Research 246, no. 1 (2015): 307–19. http://dx.doi.org/10.1016/j.ejor.2015.04.003.

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42

Enkhbat, R. "A global method for some class of optimization and control problems." International Journal of Mathematics and Mathematical Sciences 23, no. 9 (2000): 605–16. http://dx.doi.org/10.1155/s0161171200001897.

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The problem of maximizing a nonsmooth convex function over an arbitrary set is considered. Based on the optimality condition obtained by Strekalovsky in 1987 an algorithm for solving the problem is proposed. We show that the algorithm can be applied to the nonconvex optimal control problem as well. We illustrate the method by describing some computational experiments performed on a few nonconvex optimal control problems.

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Zhang, Dong, Muhammad Shoaib Saleem, Thongchai Botmart, M. S. Zahoor, and R. Bano. "Hermite–Hadamard-Type Inequalities for Generalized Convex Functions via the Caputo-Fabrizio Fractional Integral Operator." Journal of Function Spaces 2021 (November 20, 2021): 1–8. http://dx.doi.org/10.1155/2021/5640822.

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Due to applications in almost every area of mathematics, the theory of convex and nonconvex functions becomes a hot area of research for many mathematicians. In the present research, we generalize the Hermite–Hadamard-type inequalities for p , h -convex functions. Moreover, we establish some new inequalities via the Caputo-Fabrizio fractional integral operator for p , h -convex functions. Finally, the applications of our main findings are also given.

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Orlov, Andrei. "Hybrid Global Search Algorithm with Genetic Blocks for Solving Hexamatrix Games." Bulletin of Irkutsk State University. Series Mathematics 41 (2022): 40–56. http://dx.doi.org/10.26516/1997-7670.2022.41.40.

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This work addresses the development of a hybrid approach to solving threeperson polymatrix games (hexamatrix games). On the one hand, this approach is based on the reduction of the game to a nonconvex optimization problem and the Global Search Theory proposed by A.S. Strekalovsky for solving nonconvex optimization problems with (d.c.) functions representable as a difference of two convex functions. On the other hand, to increase the efficiency of one of the key stages of the global search — constructing an approximation of the level surface of a convex function that generates the basic nonconv

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Van, Nguyen Thi Thanh, Ngo Manh Tien, Nguyen Cong Luong, and Ha Thi Kim Duyen. "Energy Consumption Minimization for Autonomous Mobile Robot: A Convex Approximation Approach." Journal of Robotics and Control (JRC) 4, no. 3 (2023): 403–12. http://dx.doi.org/10.18196/jrc.v4i3.17509.

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In this paper, we consider a trajectory design problem of an autonomous mobile robot working in industrial environments. In particular, we formulate an optimization problem that jointly determines the trajectory of the robot and the time step duration to minimize the energy consumption without obstacle collisions. We consider both static and moving obstacles scenarios. The optimization problems are nonconvex, and the main contribution of this work proposing successive convex approximation (SCA) algorithms to solve the nonconvex problems with the presence of both static and moving obstacles. In

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Chen, Yang, Masao Yamagishi та Isao Yamada. "A Linearly Involved Generalized Moreau Enhancement of ℓ2,1-Norm with Application to Weighted Group Sparse Classification". Algorithms 14, № 11 (2021): 312. http://dx.doi.org/10.3390/a14110312.

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This paper proposes a new group-sparsity-inducing regularizer to approximate ℓ2,0 pseudo-norm. The regularizer is nonconvex, which can be seen as a linearly involved generalized Moreau enhancement of ℓ2,1-norm. Moreover, the overall convexity of the corresponding group-sparsity-regularized least squares problem can be achieved. The model can handle general group configurations such as weighted group sparse problems, and can be solved through a proximal splitting algorithm. Among the applications, considering that the bias of convex regularizer may lead to incorrect classification results espec

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Xu, Jiahao, Yaozhong Wang, and Wenguang Zhang. "Containment Control for High-Order Heterogeneous Continuous-Time Multi-Agent Systems with Input Nonconvex Constraints." Mathematics 13, no. 3 (2025): 509. https://doi.org/10.3390/math13030509.

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This article investigates containment control for high-order heterogeneous continuous-time multi-agent systems (MASs) with input nonconvex constraints, bounded communication delays and switching topologies. Firstly, we introduce a scaling factor for the constraint operator to obtain an equivalent unconstrained system model. Following equivalent model transformations, we analyze the maximum distance from all agents to the convex hull spanned by leaders using norm-based differentiation. It is demonstrated that, within high-order heterogeneous continuous-time MASs subject to control input nonconv

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Shen, Lixin, Bruce W. Suter, and Erin E. Tripp. "Algorithmic versatility of SPF-regularization methods." Analysis and Applications 19, no. 01 (2020): 43–69. http://dx.doi.org/10.1142/s0219530520400060.

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Sparsity promoting functions (SPFs) are commonly used in optimization problems to find solutions which are sparse in some basis. For example, the [Formula: see text]-regularized wavelet model and the Rudin–Osher–Fatemi total variation (ROF-TV) model are some of the most well-known models for signal and image denoising, respectively. However, recent work demonstrates that convexity is not always desirable in SPFs. In this paper, we replace convex SPFs with their induced nonconvex SPFs and develop algorithms for the resulting model by exploring the intrinsic structures of the nonconvex SPFs. The

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Zhou, XueGang, and JiHui Yang. "Global Optimization for the Sum of Concave-Convex Ratios Problem." Journal of Applied Mathematics 2014 (2014): 1–10. http://dx.doi.org/10.1155/2014/879739.

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This paper presents a branch and bound algorithm for globally solving the sum of concave-convex ratios problem (P) over a compact convex set. Firstly, the problem (P) is converted to an equivalent problem (P1). Then, the initial nonconvex programming problem is reduced to a sequence of convex programming problems by utilizing linearization technique. The proposed algorithm is convergent to a global optimal solution by means of the subsequent solutions of a series of convex programming problems. Some examples are given to illustrate the feasibility of the proposed algorithm.

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Dieci, L., Fabio V. Difonzo, and N. Sukumar. "Nonnegative moment coordinates on finite element geometries." Mathematics in Engineering 6, no. 1 (2024): 81–99. http://dx.doi.org/10.3934/mine.2024004.

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<abstract><p>In this paper, we introduce new generalized barycentric coordinates (coined as <italic>moment coordinates</italic>) on convex and nonconvex quadrilaterals and convex hexahedra with planar faces. This work draws on recent advances in constructing interpolants to describe the motion of the Filippov sliding vector field in nonsmooth dynamical systems, in which nonnegative solutions of signed matrices based on (partial) distances are studied. For a finite element with $ n $ vertices (nodes) in $ \mathbb{R}^2 $, the constant and linear reproducing conditions are

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