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Journal articles on the topic 'Convex constrained optimization'

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Published: 14 March 2023

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1

Zhuang, Yongjie, and Yangfan Liu. "A constrained adaptive active noise control filter design method via online convex optimization." Journal of the Acoustical Society of America 152, no. 4 (October 2022): A98. http://dx.doi.org/10.1121/10.0015669.

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In practical active noise control (ANC) applications, various types of constraints may need to be satisfied, e.g., robust stability, disturbance enhancement, and filter output power constraint. Some adaptive filters such as leaky LMS have been developed to apply required constraints indirectly. However, when multiple constraints are required simultaneously, satisfactory noise performance is difficult to achieve by tuning only one leaky factor. Another filter design approach that may achieve better noise control performance is to solve a constrained optimization problem. But the computational complexity of solving such a constrained optimization problem for ANC applications is usually too high even for offline design. Recently, a convex optimization reformulation is proposed which significantly reduces the required computational effort in solving constrained optimization problems for active noise control applications. In the current work, a constrained adaptive ANC filter design method is proposed. The previously proposed convex formulation is improved so that it can be implemented in real-time. The optimal filter coefficients are then redesigned continuously using online convex optimization when the environment is time-varying.

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2

Yu, Chun-Mei, Dang-Jun Zhao, and Ye Yang. "Efficient Convex Optimization of Reentry Trajectory via the Chebyshev Pseudospectral Method." International Journal of Aerospace Engineering 2019 (May 2, 2019): 1–9. http://dx.doi.org/10.1155/2019/1414279.

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A novel sequential convex (SCvx) optimization scheme via the Chebyshev pseudospectral method is proposed for efficiently solving the hypersonic reentry trajectory optimization problem which is highly constrained by heat flux, dynamic pressure, normal load, and multiple no-fly zones. The Chebyshev-Gauss Legend (CGL) node points are used to transcribe the original dynamic constraint into algebraic equality constraint; therefore, a nonlinear programming (NLP) problem is concave and time-consuming to be solved. The iterative linearization and convexification techniques are proposed to convert the concave constraints into convex constraints; therefore, a sequential convex programming problem can be efficiently solved by convex algorithms. Numerical results and a comparison study reveal that the proposed method is efficient and effective to solve the problem of reentry trajectory optimization with multiple constraints.

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3

Iiduka, Hideaki. "Decentralized hierarchical constrained convex optimization." Optimization and Engineering 21, no. 1 (June 1, 2019): 181–213. http://dx.doi.org/10.1007/s11081-019-09440-7.

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4

Owens, R. W., and V. P. Sreedharan. "An algorithm for constrained convex optimization." Numerical Functional Analysis and Optimization 8, no. 1-2 (January 1985): 137–52. http://dx.doi.org/10.1080/01630568508816207.

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5

Cvitanic, Jaksa, and Ioannis Karatzas. "Convex Duality in Constrained Portfolio Optimization." Annals of Applied Probability 2, no. 4 (November 1992): 767–818. http://dx.doi.org/10.1214/aoap/1177005576.

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6

Donato, Maria Bernadette. "Generalized Lagrange multiplier rule for non-convex vector optimization problems." Proceedings of the Royal Society of Edinburgh: Section A Mathematics 146, no. 2 (March 3, 2016): 297–308. http://dx.doi.org/10.1017/s0308210515000463.

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In this paper a non-convex vector optimization problem among infinite-dimensional spaces is presented. In particular, a generalized Lagrange multiplier rule is formulated as a necessary and sufficient optimality condition for weakly minimal solutions of a constrained vector optimization problem, without requiring that the ordering cone that defines the inequality constraints has non-empty interior. This paper extends the result of Donato (J. Funct. Analysis261 (2011), 2083–2093) to the general setting of vector optimization by introducing a constraint qualification assumption that involves the Fréchet differentiability of the maps and the tangent cone to the image set. Moreover, the constraint qualification is a necessary and sufficient condition for the Lagrange multiplier rule to hold.

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7

Zhang, Qiang, Shurong Li, and Jianxin Guo. "Minimum Time Trajectory Optimization of CNC Machining with Tracking Error Constraints." Abstract and Applied Analysis 2014 (2014): 1–15. http://dx.doi.org/10.1155/2014/835098.

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An off-line optimization approach of high precision minimum time feedrate for CNC machining is proposed. Besides the ordinary considered velocity, acceleration, and jerk constraints, dynamic performance constraint of each servo drive is also considered in this optimization problem to improve the tracking precision along the optimized feedrate trajectory. Tracking error is applied to indicate the servo dynamic performance of each axis. By using variable substitution, the tracking error constrained minimum time trajectory planning problem is formulated as a nonlinear path constrained optimal control problem. Bang-bang constraints structure of the optimal trajectory is proved in this paper; then a novel constraint handling method is proposed to realize a convex optimization based solution of the nonlinear constrained optimal control problem. A simple ellipse feedrate planning test is presented to demonstrate the effectiveness of the approach. Then the practicability and robustness of the trajectory generated by the proposed approach are demonstrated by a butterfly contour machining example.

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8

Liu, An, Vincent K. N. Lau, and Borna Kananian. "Stochastic Successive Convex Approximation for Non-Convex Constrained Stochastic Optimization." IEEE Transactions on Signal Processing 67, no. 16 (August 15, 2019): 4189–203. http://dx.doi.org/10.1109/tsp.2019.2925601.

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9

Ahmadi, Mohamadreza, Ugo Rosolia, Michel D. Ingham, Richard M. Murray, and Aaron D. Ames. "Constrained Risk-Averse Markov Decision Processes." Proceedings of the AAAI Conference on Artificial Intelligence 35, no. 13 (May 18, 2021): 11718–25. http://dx.doi.org/10.1609/aaai.v35i13.17393.

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We consider the problem of designing policies for Markov decision processes (MDPs) with dynamic coherent risk objectives and constraints. We begin by formulating the problem in a Lagrangian framework. Under the assumption that the risk objectives and constraints can be represented by a Markov risk transition mapping, we propose an optimization-based method to synthesize Markovian policies that lower-bound the constrained risk-averse problem. We demonstrate that the formulated optimization problems are in the form of difference convex programs (DCPs) and can be solved by the disciplined convex-concave programming (DCCP) framework. We show that these results generalize linear programs for constrained MDPs with total discounted expected costs and constraints. Finally, we illustrate the effectiveness of the proposed method with numerical experiments on a rover navigation problem involving conditional-value-at-risk (CVaR) and entropic-value-at-risk (EVaR) coherent risk measures.

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10

Kallio, Markku, and Seppo Salo. "Tatonnement Procedures for Linearly Constrained Convex Optimization." Management Science 40, no. 6 (June 1994): 788–97. http://dx.doi.org/10.1287/mnsc.40.6.788.

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11

Ahmed, Shabbir. "Convex relaxations of chance constrained optimization problems." Optimization Letters 8, no. 1 (February 21, 2013): 1–12. http://dx.doi.org/10.1007/s11590-013-0624-7.

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12

Mousavi, Seyedahmad, and Jinglai Shen. "Solution uniqueness of convex piecewise affine functions based optimization with applications to constrained ℓ1 minimization." ESAIM: Control, Optimisation and Calculus of Variations 25 (2019): 56. http://dx.doi.org/10.1051/cocv/2018061.

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In this paper, we study the solution uniqueness of an individual feasible vector of a class of convex optimization problems involving convex piecewise affine functions and subject to general polyhedral constraints. This class of problems incorporates many important polyhedral constrained ℓ1 recovery problems arising from sparse optimization, such as basis pursuit, LASSO, and basis pursuit denoising, as well as polyhedral gauge recovery. By leveraging the max-formulation of convex piecewise affine functions and convex analysis tools, we develop dual variables based necessary and sufficient uniqueness conditions via simple and yet unifying approaches; these conditions are applied to a wide range of ℓ1 minimization problems under possible polyhedral constraints. An effective linear program based scheme is proposed to verify solution uniqueness conditions. The results obtained in this paper not only recover the known solution uniqueness conditions in the literature by removing restrictive assumptions but also yield new uniqueness conditions for much broader constrained ℓ1-minimization problems.

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13

COMBETTES, PATRICK L., and JEAN-CHRISTOPHE PESQUET. "WAVELET-CONSTRAINED IMAGE RESTORATION." International Journal of Wavelets, Multiresolution and Information Processing 02, no. 04 (December 2004): 371–89. http://dx.doi.org/10.1142/s0219691304000688.

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Image restoration problems can naturally be cast as constrained convex programming problems in which the constraints arise from a priori information and the observation of signals physically related to the image to be recovered. In this paper, the focus is placed on the construction of constraints based on wavelet representations. Using a mix of statistical and convex-analytical tools, we propose a general framework to construct wavelet-based constraints. The resulting optimization problem is then solved with a block-iterative parallel algorithm which offers great flexibility in terms of implementation. Numerical results illustrate an application of the proposed framework.

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14

Radojković, Vuk, and Igor Schreiber. "Constrained stoichiometric network analysis." Physical Chemistry Chemical Physics 20, no. 15 (2018): 9910–21. http://dx.doi.org/10.1039/c8cp00528a.

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15

Jansson, Olli, and Matthew W. Harris. "Convex Optimization-Based Techniques for Trajectory Design and Control of Nonlinear Systems with Polytopic Range." Aerospace 10, no. 1 (January 10, 2023): 71. http://dx.doi.org/10.3390/aerospace10010071.

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This paper presents new techniques for the trajectory design and control of nonlinear dynamical systems. The technique uses a convex polytope to bound the range of the nonlinear function and associates with each vertex an auxiliary linear system. Provided controls associated with the linear systems can be generated to satisfy an ordering constraint, the nonlinear control is computable by the interpolation of controls obtained by convex optimization. This theoretical result leads to two numerical approaches for solving the nonlinear constrained problem: one requires solving a single convex optimization problem and the other requires solving a sequence of convex optimization problems. The approaches are applied to two practical problems in aerospace engineering: a constrained relative orbital motion problem and an attitude control problem. The solve times for both problems and approaches are on the order of seconds. It is concluded that these techniques are rigorous and of practical use in solving nonlinear trajectory design and control problems.

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16

RHANIZAR, Bouchta. "Superlinear Convergence of a Modified Newton's Method for Convex Optimization Problems With Constraints." Journal of Mathematics Research 13, no. 2 (March 24, 2021): 90. http://dx.doi.org/10.5539/jmr.v13n2p90.

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We consider the constrained optimization problem  defined by: $$f (x^*) = \min_{x \in  X} f(x)\eqno (1)$$ where the function  f : \pmb{\mathbb{R}}^{n} → \pmb{\mathbb{R}} is convex  on a closed bounded convex set X. To solve problem (1), most methods transform this problem into a problem without constraints, either by introducing Lagrange multipliers or a projection method. The purpose of this paper is to give a new method to solve some constrained optimization problems, based on the definition of a descent direction and a step while remaining in the X convex domain. A convergence theorem is proven. The paper ends with some numerical examples.

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17

Yu, Hao, and Vincent K. N. Lau. "Rank-Constrained Schur-Convex Optimization With Multiple Trace/Log-Det Constraints." IEEE Transactions on Signal Processing 59, no. 1 (January 2011): 304–14. http://dx.doi.org/10.1109/tsp.2010.2084997.

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18

Li, Chong, K. F. Ng, and T. K. Pong. "Constraint Qualifications for Convex Inequality Systems with Applications in Constrained Optimization." SIAM Journal on Optimization 19, no. 1 (January 2008): 163–87. http://dx.doi.org/10.1137/060676982.

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19

Geletu, Abebe, Armin Hoffmann, Patrick Schmidt, and Pu Li. "Chance constrained optimization of elliptic PDE systems with a smoothing convex approximation." ESAIM: Control, Optimisation and Calculus of Variations 26 (2020): 70. http://dx.doi.org/10.1051/cocv/2019077.

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In this paper, we consider chance constrained optimization of elliptic partial differential equation (CCPDE) systems with random parameters and constrained state variables. We demonstrate that, under standard assumptions, CCPDE is a convex optimization problem. Since chance constrained optimization problems are generally nonsmooth and difficult to solve directly, we propose a smoothing inner-outer approximation method to generate a sequence of smooth approximate problems for the CCPDE. Thus, the optimal solution of the convex CCPDE is approximable through optimal solutions of the inner-outer approximation problems. A numerical example demonstrates the viability of the proposed approach.

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20

Flamant, Julien, Sebastian Miron, and David Brie. "A General Framework for Constrained Convex Quaternion Optimization." IEEE Transactions on Signal Processing 70 (2022): 254–67. http://dx.doi.org/10.1109/tsp.2021.3137746.

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21

Zhao, You, Xiaofeng Liao, and Xing He. "Novel projection neurodynamic approaches for constrained convex optimization." Neural Networks 150 (June 2022): 336–49. http://dx.doi.org/10.1016/j.neunet.2022.03.011.

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22

Gonzaga, Clóvis C., Elizabeth W. Karas, and Diane R. Rossetto. "An Optimal Algorithm for Constrained Differentiable Convex Optimization." SIAM Journal on Optimization 23, no. 4 (January 2013): 1939–55. http://dx.doi.org/10.1137/110836602.

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23

Labbé, Chantal, and Andrew J. Heunis. "Convex duality in constrained mean-variance portfolio optimization." Advances in Applied Probability 39, no. 1 (March 2007): 77–104. http://dx.doi.org/10.1239/aap/1175266470.

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We apply conjugate duality to establish the existence of optimal portfolios in an asset-allocation problem, with the goal of minimizing the variance of the final wealth which results from trading over a fixed, finite horizon in a continuous-time, complete market, subject to the constraints that the expected final wealth equal a specified target value and the portfolio of the investor (defined by the dollar amount invested in each stock) take values in a given closed, convex set. The asset prices are modelled by Itô processes, for which the market parameters are random processes adapted to the information filtration available to the investor. We synthesize a dual optimization problem and establish a set of optimality relations, similar to the Euler-Lagrange and transversality relations of calculus of variations, giving necessary and sufficient conditions for the given optimization problem and its dual to each have a solution, with zero duality gap. We then solve these relations, to establish the existence of an optimal portfolio.

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24

Konsulova, A. S., and J. P. Revalski. "Constrained convex optimization problems-well-posedness and stability*." Numerical Functional Analysis and Optimization 15, no. 7-8 (January 1994): 889–907. http://dx.doi.org/10.1080/01630569408816598.

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25

Labbé, Chantal, and Andrew J. Heunis. "Convex duality in constrained mean-variance portfolio optimization." Advances in Applied Probability 39, no. 01 (March 2007): 77–104. http://dx.doi.org/10.1017/s0001867800001610.

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We apply conjugate duality to establish the existence of optimal portfolios in an asset-allocation problem, with the goal of minimizing the variance of the final wealth which results from trading over a fixed, finite horizon in a continuous-time, complete market, subject to the constraints that the expected final wealth equal a specified target value and the portfolio of the investor (defined by the dollar amount invested in each stock) take values in a given closed, convex set. The asset prices are modelled by Itô processes, for which the market parameters are random processes adapted to the information filtration available to the investor. We synthesize a dual optimization problem and establish a set of optimality relations, similar to the Euler-Lagrange and transversality relations of calculus of variations, giving necessary and sufficient conditions for the given optimization problem and its dual to each have a solution, with zero duality gap. We then solve these relations, to establish the existence of an optimal portfolio.

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26

Sznaier, Mario, and Franco Blanchini. "Robust control of constrained systems via convex optimization." International Journal of Robust and Nonlinear Control 5, no. 5 (1995): 441–60. http://dx.doi.org/10.1002/rnc.4590050506.

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27

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 distributed computation, we then exploit the exact penalty function method to transform the sequence of convex constrained subproblems into unconstrained ones. Finally, a fully distributed method is designed to solve the unconstrained subproblems. The convergence of the proposed algorithm is rigorously established, which shows that the algorithm can converge asymptotically to a stationary solution of the problem under consideration. Several simulation results are illustrated to show the performance of the proposed method.

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28

Sahoo, Laxminarayan, Supriyan Sen, Kalishankar Tiwary, Sovan Samanta, and Tapan Senapati. "Optimization of Data Distributed Network System under Uncertainty." Discrete Dynamics in Nature and Society 2022 (April 8, 2022): 1–12. http://dx.doi.org/10.1155/2022/7806083.

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The major network design or data distributed problems may be described as constrained optimization problems. Constrained optimization problems include restrictions imposed by the system designers. These limitations are basically due to the system design’s physical limitations or functional requirements of the network system. Constrained optimization is a computationally challenging job whenever the constraints/limitations are nonlinear and nonconvex. Furthermore, nonlinear programming methods can easily deal same optimization problem if somehow the constraints are nonlinear and convex. In this paper, we have addressed a distributed network design problem involving uncertainty that transmits data across a parallel router. This distributed network design problem is a Jackson open-type network design problem that has been formulated based on the M/M/1 queueing system. Because our network design problem is a nonlinear, convex optimization problem, we have employed a well-known Kuhn–Tucker (K-T) optimality algorithm to solve the same. Here, we have used triangular fuzzy numbers to express uncertain traffic rates and data processing rates. Then, by applying α -level interval of fuzzy numbers and their corresponding parametric representation of α -level intervals, the associated network design problem has been transformed to its parametric form and later has been solved. To obtain the optimal data stream rate in terms of interval and to illustrate the applicability of the entire approach, a hypothetical numerical example has been exhibited. Finally, the most important results have been reported.

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29

Sumin, M. I. "On the regularization of the Lagrange principle and on the construction of the generalized minimizing sequences in convex constrained optimization problems." Vestnik Udmurtskogo Universiteta. Matematika. Mekhanika. Komp'yuternye Nauki 30, no. 3 (September 2020): 410–28. http://dx.doi.org/10.35634/vm200305.

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We consider the regularization of the Lagrange principle (LP) in the convex constrained optimization problem with operator constraint-equality in a Hilbert space and with a finite number of functional inequality-constraints. The objective functional of the problem is not, generally speaking, strongly convex. The set of admissible elements of the problem is also embedded into a Hilbert space and is not assumed to be bounded. Obtaining a regularized LP is based on the dual regularization method and involves the use of two regularization parameters and two corresponding matching conditions at the same time. One of the regularization parameters is «responsible» for the regularization of the dual problem, while the other is contained in a strongly convex regularizing addition to the objective functional of the original problem. The main purpose of the regularized LP is the stable generation of generalized minimizing sequences that approximate the exact solution of the problem by function and by constraint, for the purpose of its practical stable solving.

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LI, JUEYOU, CHANGZHI WU, ZHIYOU WU, QIANG LONG, and XIANGYU WANG. "DISTRIBUTED PROXIMAL-GRADIENT METHOD FOR CONVEX OPTIMIZATION WITH INEQUALITY CONSTRAINTS." ANZIAM Journal 56, no. 2 (October 2014): 160–78. http://dx.doi.org/10.1017/s1446181114000273.

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AbstractWe consider a distributed optimization problem over a multi-agent network, in which the sum of several local convex objective functions is minimized subject to global convex inequality constraints. We first transform the constrained optimization problem to an unconstrained one, using the exact penalty function method. Our transformed problem has a smaller number of variables and a simpler structure than the existing distributed primal–dual subgradient methods for constrained distributed optimization problems. Using the special structure of this problem, we then propose a distributed proximal-gradient algorithm over a time-changing connectivity network, and establish a convergence rate depending on the number of iterations, the network topology and the number of agents. Although the transformed problem is nonsmooth by nature, our method can still achieve a convergence rate, ${\mathcal{O}}(1/k)$, after $k$ iterations, which is faster than the rate, ${\mathcal{O}}(1/\sqrt{k})$, of existing distributed subgradient-based methods. Simulation experiments on a distributed state estimation problem illustrate the excellent performance of our proposed method.

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31

Bian, Jinhong, YuanYuan Wang, and Feng Zhou. "Secrecy Energy Efficiency Optimization for Reconfigurable Intelligent Surface-Aided Multiuser MISO Systems." Wireless Communications and Mobile Computing 2022 (October 7, 2022): 1–11. http://dx.doi.org/10.1155/2022/5498172.

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Currently, the reconfigurable intelligent surface (RIS) has been applied to improve the physical layer security in wireless networks. In this paper, we focus on the secure transmission in RIS-aided multiple-input single-output (MISO) systems. Specifically, by assuming that only imperfect channel state information (CSI) of the eavesdropper can be obtained, we investigated the robust secrecy energy efficiency (SEE) optimization via jointly designing the active beamforming (BF), artificial noise (AN) at Alice, and the passive phase shifter at the RIS. The formulated problem is hard to handle due to the complicated secrecy rate expression as well as the infinite constraints introduced by the CSI uncertainties. By utilizing the Taylor expansion, we transformed the fractional programming into a convex problem, while all the constraints are approximated via the successive convex approximation and constrained concave-convex procedure. Then, by using the extended S-Lemma, we transform the infinite constraints into linear matrix inequality, which is convex. Finally, an alternate optimization (AO) algorithm was proposed to solve the reformulated problem. Simulation results demonstrated the performance of the proposed design.

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32

Yuan, Jing, Juan Shi, and Xue-Cheng Tai. "A Convex and Exact Approach to Discrete Constrained TV-L1 Image Approximation." East Asian Journal on Applied Mathematics 1, no. 2 (May 2011): 172–86. http://dx.doi.org/10.4208/eajam.220310.181110a.

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AbstractWe study the TV-L1 image approximation model from primal and dual perspective, based on a proposed equivalent convex formulations. More specifically, we apply a convex TV-L1 based approach to globally solve the discrete constrained optimization problem of image approximation, where the unknown image function u(x) ∈ {f1,…,fn}, ∀x ∈ Ω. We show that the TV-L1 formulation does provide an exact convex relaxation model to the non-convex optimization problem considered. This result greatly extends recent studies of Chan et al., from the simplest binary constrained case to the general gray-value constrained case, through the proposed rounding scheme. In addition, we construct a fast multiplier-based algorithm based on the proposed primal-dual model, which properly avoids variability of the concerning TV-L1 energy function. Numerical experiments validate the theoretical results and show that the proposed algorithm is reliable and effective.

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Hintermüller, M., C. N. Rautenberg, and S. Rösel. "Density of convex intersections and applications." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 473, no. 2205 (September 2017): 20160919. http://dx.doi.org/10.1098/rspa.2016.0919.

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In this paper, we address density properties of intersections of convex sets in several function spaces. Using the concept of Γ -convergence, it is shown in a general framework, how these density issues naturally arise from the regularization, discretization or dualization of constrained optimization problems and from perturbed variational inequalities. A variety of density results (and counterexamples) for pointwise constraints in Sobolev spaces are presented and the corresponding regularity requirements on the upper bound are identified. The results are further discussed in the context of finite-element discretizations of sets associated with convex constraints. Finally, two applications are provided, which include elasto-plasticity and image restoration problems.

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Metel, Michael R., and Akiko Takeda. "Primal-dual subgradient method for constrained convex optimization problems." Optimization Letters 15, no. 4 (April 5, 2021): 1491–504. http://dx.doi.org/10.1007/s11590-021-01728-x.

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35

Hassan, Mansur, and Adam Baharum. "Modified Courant-Beltrami penalty function and a duality gap for invex optimization problem." International Journal for Simulation and Multidisciplinary Design Optimization 10 (2019): A10. http://dx.doi.org/10.1051/smdo/2019010.

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In this paper, we modified a Courant-Beltrami penalty function method for constrained optimization problem to study a duality for convex nonlinear mathematical programming problems. Karush-Kuhn-Tucker (KKT) optimality conditions for the penalized problem has been used to derived KKT multiplier based on the imposed additional hypotheses on the constraint function g. A zero-duality gap between an optimization problem constituted by invex functions with respect to the same function η and their Lagrangian dual problems has also been established. The examples have been provided to illustrate and proved the result for the broader class of convex functions, termed invex functions.

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Skipper, Jack, and Emil Wiedemann. "Lower semi-continuity for 𝒜-quasiconvex functionals under convex restrictions." ESAIM: Control, Optimisation and Calculus of Variations 27 (2021): 107. http://dx.doi.org/10.1051/cocv/2021105.

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We show weak lower semi-continuity of functionals assuming the new notion of a “convexly constrained” 𝒜-quasiconvex integrand. We assume 𝒜-quasiconvexity only for functions defined on a set K which is convex. Assuming this and sufficient integrability of the sequence we show that the functional is still (sequentially) weakly lower semi-continuous along weakly convergent “convexly constrained” 𝒜-free sequences. In a motivating example, the integrand is − det1/d−1 and the convex constraint is positive semi-definiteness of a matrix field.

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Yonesie, Behrooz, Ashkan Sebghati, and Saeed Shamaghdari. "Constrained Optimal PID Controller Design: Convex-Concave Optimization Approach." Journal of Control 14, no. 1 (May 1, 2020): 1–10. http://dx.doi.org/10.29252/joc.14.1.1.

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Zhang, Yijian, Emiliano Dall'Anese, and Mingyi Hong. "Online Proximal-ADMM for Time-Varying Constrained Convex Optimization." IEEE Transactions on Signal and Information Processing over Networks 7 (2021): 144–55. http://dx.doi.org/10.1109/tsipn.2021.3051292.

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Hough, Matthew, and Lindon Roberts. "Model-Based Derivative-Free Methods for Convex-Constrained Optimization." SIAM Journal on Optimization 32, no. 4 (October 13, 2022): 2552–79. http://dx.doi.org/10.1137/21m1460971.

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Wang, Jiayao, and Haibin Shang. "Constrained Spacecraft Attitude Optimal Control via Successive Convex Optimization." Journal of Physics: Conference Series 2095, no. 1 (November 1, 2021): 012039. http://dx.doi.org/10.1088/1742-6596/2095/1/012039.

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Abstract Rapid attitude path planning is the key technique in autonomous spacecraft operation missions. An efficient method is proposed for energy-optimal spacecraft attitude control in presence of constraints. Firstly, Gauss pseudospectral method is utilized to discretize and transcribe the primal continuous problem to a nonlinear programming problem. Then a set of convexification techniques are used to convexity the nonlinear programming problem to a series of second-order cone programming problems, which can be solved iteratively by the interior-point method. A solution to the nonlinear programming problem is obtained as the iteration converges. Numerical results show the method could obtain a valid energy-optimal attitude control plan more rapidly than traditional methods.

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Chen, Caihua, Raymond H. Chan, Shiqian Ma, and Junfeng Yang. "Inertial Proximal ADMM for Linearly Constrained Separable Convex Optimization." SIAM Journal on Imaging Sciences 8, no. 4 (January 2015): 2239–67. http://dx.doi.org/10.1137/15100463x.

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Chatzipanagiotis, Nikolaos, and Michael M. Zavlanos. "A Distributed Algorithm for Convex Constrained Optimization Under Noise." IEEE Transactions on Automatic Control 61, no. 9 (September 2016): 2496–511. http://dx.doi.org/10.1109/tac.2015.2504932.

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Buijs, J., J. Suykens, and B. De Moor. "Model Predictive Control: Convex Optimization Versus Constrained Dynamic Backpropagation." IFAC Proceedings Volumes 34, no. 22 (November 2001): 343–47. http://dx.doi.org/10.1016/s1474-6670(17)32962-2.

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Van Voorhis, Tim, and Faiz A. Al-Khayyal. "Difference of convex solution of quadratically constrained optimization problems." European Journal of Operational Research 148, no. 2 (July 2003): 349–62. http://dx.doi.org/10.1016/s0377-2217(02)00432-0.

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Karas, Elizabeth, Ademir Ribeiro, Claudia Sagastizábal, and Mikhail Solodov. "A bundle-filter method for nonsmooth convex constrained optimization." Mathematical Programming 116, no. 1-2 (April 28, 2007): 297–320. http://dx.doi.org/10.1007/s10107-007-0123-7.

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Bello, Lenys, and Marcos Raydan. "Convex constrained optimization for the seismic reflection tomography problem." Journal of Applied Geophysics 62, no. 2 (June 2007): 158–66. http://dx.doi.org/10.1016/j.jappgeo.2006.10.004.

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Pinar, Mustafa Ç., and Stavros A. Zenios. "On Smoothing Exact Penalty Functions for Convex Constrained Optimization." SIAM Journal on Optimization 4, no. 3 (August 1994): 486–511. http://dx.doi.org/10.1137/0804027.

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Zhang, Jianzhong, and Chengxian Xu. "Inverse optimization for linearly constrained convex separable programming problems." European Journal of Operational Research 200, no. 3 (February 2010): 671–79. http://dx.doi.org/10.1016/j.ejor.2009.01.043.

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Peng, Yehui, and Zhenhai Liu. "A variable metric method for nonsmooth convex constrained optimization." Applied Mathematics and Computation 183, no. 2 (December 2006): 961–71. http://dx.doi.org/10.1016/j.amc.2006.05.132.

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Amer, Mohamed R., Siavash Yousefi, Raviv Raich, and Sinisa Todorovic. "Monocular Extraction of 2.1D Sketch Using Constrained Convex Optimization." International Journal of Computer Vision 112, no. 1 (August 10, 2014): 23–42. http://dx.doi.org/10.1007/s11263-014-0752-2.

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