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A modified exact smooth penalty function for nonlinear constrained optimization

JOURNAL OF INEQUALITIES AND APPLICATIONS 2012年第1期2012卷 1-11页

作者： Liu Bingzhuang Zhao Wenling Shandong Univ Technol Sch Sci Zibo 255049 Shandong Peoples R China

In this paper, a modified simple penalty function is proposed for a constrained nonlinear programming problem by augmenting the dimension of the program with a variable that controls the weight of the penalty terms. This penalty function enjoys improved smoothness. Under mild conditions, it can be proved to be exact in the sense that local minimizers of the original constrained problem are precisely the local minimizers of the associated penalty problem.

关键词： constrained minimization exact penalty function nonlinear programming problem

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3D irregular packing in an optimized cuboid container

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IFAC-PapersOnLine 2019年第13期52卷 2014-2019页

作者： Litvinchev, I. Pankratov, A. Romanova, T. Faculty of Mechanical and Electrical Engineering San Nicolas de los Garza Mexico Institute for Mechanical Engineering Problems of the National Academy of Sciences of Ukraine Department of Mathematical Modelling and Optimal Design Kharkiv Ukraine

A packing problem for irregular 3D objects approximated by polyhedra is presented. The objects have to be packed into a cuboid of minimum height under continuous rotations, translations and minimum allowable distances between objects. The problem has various applications and arises, e.g. in additive manufacturing. Containment, distance and non-overlapping constraints are described using the phi-function technique. The irregular packing problem is formulated in the form of nonlinear programming problem. A solution algorithm is proposed based on a fast starting point algorithm and efficient local optimization procedure. © 2019, IFAC (International Federation of Automatic Control) Hosting by Elsevier Ltd. All rights reserved.

关键词： 3D printers Mathematical models nonlinear programming 3 D printing Continuous rotation Local optimizations Non linear optimization nonlinear programming problem Operation research Overlapping constraints Solution algorithms

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First- and Second-Order Necessary Conditions Via Exact Penalty Functions

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JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS 2015年第3期165卷 720-752页

作者： Meng, Kaiwen Yang, Xiaoqi Southwest Jiaotong Univ Sch Econ & Management Chengdu 610031 Peoples R China Hong Kong Polytech Univ Dept Appl Math Kowloon Hong Kong Peoples R China

In this paper, we study first- and second-order necessary conditions for nonlinear programming problems from the viewpoint of exact penalty functions. By applying the variational description of regular subgradients, we first establish necessary and sufficient conditions for a penalty term to be of KKT-type by using the regular subdifferential of the penalty term. In terms of the kernel of the subderivative of the penalty term, we also present sufficient conditions for a penalty term to be of KKT-type. We then derive a second-order necessary condition by assuming a second-order constraint qualification, which requires that the second-order linearized tangent set is included in the closed convex hull of the kernel of the parabolic subderivative of the penalty term. In particular, for a penalty term with order , by assuming the nonpositiveness of a sum of a second-order derivative and a third-order derivative of the original data and applying a third-order Taylor expansion, we obtain the second-order necessary condition.

关键词： nonlinear programming problem KKT condition Second-order necessary condition Subderivative Regular subdifferential

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A Supply Restoration Method of Distribution System Based on Soft Open Point

A Supply Restoration Method of Distribution System Based on ...

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IEEE Innovative Smart Grid Technologies - Asia (ISGT-Asia)

作者： Li, Peng Song, Guanyu Ji, Haoran Zhao, Jinli Wang, Chengshan Wu, Jianzhong Tianjin Univ Minist Educ Key Lab Smart Grid Tianjin Peoples R China Cardiff Univ Sch Engn Inst Energy Cardiff S Glam Wales

ISBN: (纸本)9781509043033

Soft Open Point (SOP) refers to a novel power electronic device installed in distribution system to replace the traditional tie switch. The application of SOP will promote the flexibility and resilience of the distribution system. Under a fault condition, SOP enables to provide voltage support and helps to expand the scope of power supply for the supply restoration. In this paper, a supply restoration model of distribution system is established based on SOP, which is essentially a complex nonlinear programming problem. The primal-dual interior-point algorithm is adopted to solve the problem, which can find the optimal solution rapidly and accurately. Then, the modified IEEE 33-node system is used to verify the effectiveness and efficiency of the proposed method.

关键词： distribution system Soft Open Point (SOP) supply restoration nonlinear programming problem primal-dual interior-point algorithm

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Power system state estimation: A new method based on current equations

Power system state estimation: A new method based on current...

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Large Engineering Systems Conference on Power Engineering

作者： Lavorato, Marina Rider, Marcos J. Garcia, Ariovaldo V. Univ Estadual Campinas Dept Elect Energy Syst Campinas SP Brazil

ISBN: (纸本)9781424415823

This paper proposes a new state estimation method modeled as a nonlinear programming problem with equality constraints. The majority of the estimated state estimation methods work with a set of measurements composed of active and reactive power flows on branches, active and reactive injection power on nodes, and nodal voltage magnitudes. In this method, the current magnitude branch measurements are considered in a simpler and direct manner, increasing the global redundancy of the system. Tests were carried out with several systems widely known in the literature and the results obtained confirmed the efficiency of the method. The method can be applied both to transmission and distribution systems and permit the inclusion of the inequality constraints and the bad data processing.

关键词： state estimation current equations model nonlinear programming problem power systems current measurement

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Switched System Optimal Control Based on Parameterizations of the Control Vectors and Switching Instants

Switched System Optimal Control Based on Parameterizations o...

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23rd Chinese Control and Decision Conference

作者： Zhao, Rui-yan Li, Shu-rong China Univ Petr Coll Informat & Control Engn Dongying 257061 Peoples R China

ISBN: (纸本)9781424487363

This paper presents a new,approach for solving optimal control problems for switched systems with prespecified order of the sequence of subsystems. For such problems, we need to seek both the optimal switching instants and the optimal continuous inputs. The optimal control problem for hybrid systems is transcribed into an equivalent problem parameterized by the switching instants and the control vectors. Through the discretization of the control space, the control vector is approximated by the B-spline functions. In order to search for the optimal switching instants, we introduce the normalized time variable and do normalized treatment for the control arcs. The optimal switching control problem is converted to a nonlinear programming problem. The control profiles and switching instants act as decision variables. Two examples are solved using the proposed method so as to demonstrate the effectiveness of the method proposed.

关键词： Switched systems Optimal control problem B-spline functions nonlinear programming problem

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On the costwise optimality of hierarchical multiresponse randomized block designs under the trace criterion

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Annals of the Institute of Statistical Mathematics 1969年第1期21卷 507-514页

作者： Srivastava, J.N. McDonald, L.L. Colorado State University United States

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nonlinear programming in Banach spaces

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Journal of Optimization Theory and Applications 1969年第3期4卷 182-190页

作者： Nagahisa, Youji Sakawa, Yoshiyuki Faculty of Engineering Yamaguchi University Ube Yamaguchi Japan Faculty of Engineering Science Osaka University Toyonaka Osaka Japan

This paper is devoted to the formulation of generalized nonlinear programming problems in Banach spaces and to the derivation of the necessary conditions which the solutions of these problems must satisfy. © 1969... 详细信息

关键词： Banach Space programming problem nonlinear programming nonlinear programming problem Generalize nonlinear programming

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State Estimation for Unbalanced Three-Phase AC Microgrids Based on Mathematical programming

State Estimation for Unbalanced Three-Phase AC Microgrids Ba...

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IEEE-Power-and-Energy-Society Innovative Smart Grid Technologies Conference (ISGT)

作者： Acuna Acurio, Byron Alejandro Cherrez Barragan, Diana Estefania Lopez, Juan Camilo Grijalva, Felipe Rodriguez, Juan Carlos Pereira da Silva, Luiz Carlos Univ Campinas UNICAMP Campinas SP Brazil Univ San Francisco Quito Quito Ecuador Analog Devices Inc Wilmington MA USA

ISBN: (纸本)9781665453554

State estimation (SE) helps to determine the most-likely steady-state operation of microgrids based on field measurements. It is a fundamental data processing tool responsible for supporting and increasing system visibility and filtering errors that may appear in real-time measurements, system topology, and parameters. Hence, it serves as a reliable basis for the energy management system (EMS) infrastructure. Existing SE methods are based on Newton-like algorithms rather than using specific optimization. Nevertheless, SE can always be reduced to a constrained optimization problem, with the objective of minimizing a given criterion, e.g., weighted least squares (WLS) or weighted least absolute value (WLAV). In this context, this paper presents two unbalanced three-phase AC SE methods based on mathematical programming for microgrids. The effectiveness and validity of the proposed state estimation approach are demonstrated on a real microgrid located at the State University of Campinas, in Brazil, and over one widely known IEEE test system. The method can be easily adapted to other microgrids with different configurations, distributed energy resources, and measurements. Results show that the proposed methods report high accuracy, but the state estimator based on WLS is faster than the WLAV.

关键词： Microgrids state estimation nonlinear programming problem unbalanced three-phase AC network

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Semi-mechanization Method for a Unsolved Optimization problem in Combinatorial Geometry 07

Semi-mechanization Method for a Unsolved Optimization Proble...

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22nd ACM Symposium on Applied Computing

作者： Zeng, Zhenbing Shan, Meijing E China Normal Univ Inst Software Engn Shanghai 200062 Peoples R China

ISBN: (纸本)9781595934802

This paper presents a new semi-mechanization method for proving the validity of an inequality conjecture about convex n-gon when n = 8 and gaining headway in proving it when n = 9. This conjecture is generally converted into a global optimization problem which is related to Heilbronn triangular problem. For solving it, the bottleneck is the complexity increasing very quickly with n. In the proposed algorithm, to reduce the dimension of freedom we first analyze the properties of the optimal configurations and try to obtain the strict polynomial inequality and equality conditions as many as possible. After the precondition, the mechanization method can be implemented to solve this nonlinear optimization problem, so we call the overall approach as semi-mechanization method. We hope our algorithm will be useful for proving the conjecture with larger value of n.

关键词： semi-mechanization method Heilbronn triangular problem nonlinear programming problem combinatorial geometry

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