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8th International Tri-Annual Conference on Optimization - Techniques and Applications (ICOTA)

作者： Fowkes, Jaroslav M. Gould, Nicholas I. M. Farmer, Chris L. Univ Edinburgh Sch Math Edinburgh EH9 3JZ Midlothian Scotland Rutherford Appleton Lab Computat Sci & Engn Dept Chilton OX11 0QX Oxon England Univ Oxford Math Inst Oxford OX1 3LB England

We present a branch and bound algorithm for the global optimization of a twice differentiable nonconvex objective function with a Lipschitz continuous Hessian over a compact, convex set. The algorithm is based on applying cubic regularisation techniques to the objective function within an overlapping branch and bound algorithm for convex constrained global optimization. Unlike other branch and bound algorithms, lower bounds are obtained via nonconvex underestimators of the function. For a numerical example, we apply the proposed branch and bound algorithm to radial basis function approximations.

关键词： Global optimization Lipschitzian optimization Branch and bound nonconvex programming

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On programming with absolute-value functions

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Journal of Optimization Theory and Applications 1975年第1-2期17卷 181-183页

作者： Hill Jr., T.W. Ravindran, A. AiResearch Manufacturing Company of Arizona Phoenix Arizona United States Purdue University West Lafayette Indiana United States

This paper considers some programming problems with absolute-value (objective) functions subject to linear constraints. Necessary and sufficient conditions for the existence of finite optimum solutions to these proble... 详细信息

关键词： absolute-value problems linear programming Mathematical programming nonconvex programming operations research optimality criteria

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Global Optimization of nonconvex Factorable Programs with Applications to Engineering Design Problems

Global Optimization of Nonconvex Factorable Programs with Ap...

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作者： Wang, Hongjie Virginia Tech | University

The primary objective of this thesis is to develop and implement a global optimization algorithm to solve a class of nonconvex programming problems, and to test it using a collection of engineering design problem *** class of problems we consider involves the optimization of a general nonconvex factorable objective function over a feasible region that is restricted by a set of constraints, each of which is defined in terms of nonconvex factorable functions. Such problems find widespread applications in production planning, location and allocation, chemical process design and control, VLSI chip design, and numerous engineering design problems. This thesis offers a first comprehensive methodological development and implementation for determining a global optimal solution to such factorable programming problems. To solve this class of problems, we propose a branch-and-bound approach based on linear programming (LP) relaxations generated through various approximation schemes that utilize, for example, the Mean-Value Theorem and Chebyshev interpolation polynomials, coordinated with a {em Reformulation-Linearization Technique} (RLT). The initial stage of the lower bounding step generates a tight, nonconvex polynomial programming relaxation for the given problem. Subsequently, an LP relaxation is constructed for the resulting polynomial program via a suitable RLT procedure. The underlying motivation for these two steps is to generate a tight outer approximation of the convex envelope of the objective function over the convex hull of the feasible region. The bounding step is thenintegrated into a general branch-and-bound framework. The construction of the bounding polynomials and the node partitioning schemes are specially designed so that the gaps resulting from these two levels of approximations approach zero in the limit, thereby ensuring convergence to a global optimum. Various implementation issues regarding the formulation of such tight bounding p

关键词： nonconvex programming global optimization nonlinear programming RLT Thesis

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Dynamics and density distribution of strongly confined noninteracting nonaligning self-propelled particles in a nonconvex boundary

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Physical Review E 2015年第1期91卷 012125-012125页

作者： Yaouen Fily Aparna Baskaran Michael F. Hagan Martin Fisher School of Physics Brandeis University Waltham Massachusetts 02453 USA

We study the dynamics of nonaligning, noninteracting self-propelled particles confined to a box in two dimensions. In the strong confinement limit, when the persistence length of the active particles is much larger than the size of the box, particles stay on the boundary and align with the local boundary normal. It is then possible to derive the steady-state density on the boundary for arbitrary box shapes. In nonconvex boxes, the nonuniqueness of the boundary normal results in hysteretic dynamics and the density is nonlocal, i.e., it depends on the global geometry of the box. These findings establish a general connection between the geometry of a confining box and the behavior of an ideal active gas it confines, thus providing a powerful tool to understand and design such confinements.

关键词： nonconvex programming DYNAMICS DENSITY HYDRODYNAMICS QUASISTATIC processes

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A Deep-Cutting-Plane Technique for Reverse Convex Optimization

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IEEE TRANSACTIONS ON SYSTEMS MAN AND CYBERNETICS PART B-CYBERNETICS 2011年第4期41卷 1054-1060页

作者： Moshirvaziri, Khosrow Amouzegar, Mahyar A. Calif State Univ Long Beach Dept Informat Syst Long Beach CA 90840 USA RAND Corp Santa Monica CA 90401 USA

A large number of problems in engineering design and in many areas of social and physical sciences and technology lend themselves to particular instances of problems studied in this paper. Cutting-plane methods have traditionally been used as an effective tool in devising exact algorithms for solving convex and large-scale combinatorial optimization problems. Its utilization in nonconvex optimization has been also promising. A cutting plane, essentially a hyperplane defined by a linear inequality, can be used to effectively reduce the computational efforts in search of a global solution. Each cut is generated in order to eliminate a large portion of the search domain. Thus, a deep cut is intuitively superior in which it will exclude a larger set of extraneous points from consideration. This paper is concerned with the development of deep-cutting-plane techniques applied to reverse-convex programs. An upper bound and a lower bound for the optimal value are found, updated, and improved at each iteration. The algorithm terminates when the two bounds collapse or all the generated subdivisions have been fathomed. Finally, computational considerations and numerical results on a set of test problems are discussed. An illustrative example, walking through the steps of the algorithm and explaining the computational process, is presented.

关键词： Cutting-plane methods global optimization nonconvex programming reverse-convex programs (RCPs)

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Energy-Efficient Power Optimization with Spectrum Sensing Errors in OFDMA Cognitive Opportunistic Relay Links

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INTERNATIONAL JOURNAL OF DISTRIBUTED SENSOR NETWORKS 2016年第2期12卷 2716042-2716042页

作者： Feng, Li Kuang, Yujun Fu, Xinchuan Wu, Binwei Univ Elect Sci & Technol China Sch Commun & Informat Engn Chengdu 611731 Peoples R China Sichuan Open Univ Chengdu 610073 Peoples R China Tsinghua Univ Tsinghua Natl Lab Informat Sci & Technol Beijing 100084 Peoples R China

We propose a novel algorithm to optimize the energy efficiency (EE) of OFDM-based cognitive opportunistic relaying links (CORL) under secondary users (SUs) incorrectly sensing the unlicensed spectrum. We formulate an optimization problem with imperfect sensing that satisfies a specified power budget for the secondary users (SUs), while restricting the interference to primary user (PU) in a statistical manner. Unlike all related works in the literature, we consider the effect of subcarrier transmission mode on the relaying links and we additionally consider the effect of limited sensing capabilities of the SUs. The optimization problem is nonconvex and it is transformed to an equivalent problem using the concept of fractional programming. With the aid of the fractional programming method, an EE-oriented power allocation policy with low complexity is proposed which adopts the bisection method to speed up the search of the optimum. Simulation results show that the EE deteriorates as the channel sensing error increases. Comparisons with relevant works from the literature show that the EE is slightly deteriorated if the SU does not account for spectrum sensing errors.

关键词： ORTHOGONAL frequency division multiplexing ENERGY consumption SUBCARRIER multiplexing FRACTIONAL programming nonconvex programming

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A Generalized Formulation for Group Selection via ADMM

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JOURNAL OF SCIENTIFIC COMPUTING 2024年第1期100卷 15-15页

作者： Ke, Chengyu Shin, Sunyoung Lou, Yifei Ahn, Miju Southern Methodist Univ Dept Operat Res & Engn Management Dallas TX 75205 USA Pohang Univ Sci & Technol Dept Math Pohang 37673 Gyeongbuk South Korea Univ North Carolina Chapel Hill Dept Math Chapel Hill NC 27599 USA Univ North Carolina Chapel Hill Sch Data Sci & Soc Chapel Hill NC 27599 USA

This paper studies a statistical learning model where the model coefficients have a pre-determined non-overlapping group sparsity structure. We consider a combination of a loss function and a regularizer to recover the desired group sparsity patterns, which can embrace many existing works. We analyze directional stationary solutions of the proposed formulation, obtaining a sufficient condition for a directional stationary solution to achieve optimality and establishing a bound of the distance from the solution to a reference point. We develop an efficient algorithm that adopts an alternating direction method of multiplier (ADMM), showing that the iterates converge to a directional stationary solution under certain conditions. In the numerical experiment, we implement the algorithm for generalized linear models with convex and nonconvex group regularizers to evaluate the model performance on various data types, noise levels, and sparsity settings.

关键词： ADMM Group sparsity Group variable selection nonconvex programming Directional stationary solutions

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Rate Dependent Response of Nanoscale Structures Having a Multiwell Energy Landscape

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Physical Review Letters 2015年第9期114卷 095504-095504页

作者： Itamar Benichou Sefi Givli Faculty of Mechanical Engineering Technion-Israel Institute of Technology Haifa 32000 Israel

A stochastic and rate-dependent response originating from thermal fluctuations over a highly nonconvex energy landscape is a prevailing aspect of the mechanical behavior of nanoscale structures. The overdamped dynamics of a bistable chain subjected to thermal fluctuations is prototypical of such behavior. Based on this approach, we find a new nondimensional quantity, similar in its mathematical structure to Boltzmann’s factor, which captures the intricate competition between rate, temperature, and energy barriers underlying the system dynamics. In turn, we obtain simple universal laws for predicting statistical properties of the mechanical response.

关键词： NANOELECTROMECHANICAL systems nonconvex programming BOLTZMANN factor SPATIAL distribution (Quantum optics) ELECTROMAGNETIC spectrum

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Dimer motion on a periodic substrate: Spontaneous symmetry breaking and absolute negative mobility

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Physical Review E 2012年第6期85卷 061132-061132页

作者： David Speer Ralf Eichhorn Mykhaylo Evstigneev Peter Reimann Universität Bielefeld Fakultät für Physik 33615 Bielefeld Germany NORDITA Roslagstullsbacken 23 10691 Stockholm Sweden

We consider two coupled particles moving along a periodic substrate potential with negligible inertia effects (overdamped limit). Even when the particles are identical and the substrate spatially symmetric, a sinusoidal external driving of appropriate amplitude and frequency may lead to spontaneous symmetry breaking in the form of a permanent directed motion of the dimer. Thermal noise restores ergodicity and thus zero net velocity, but entails arbitrarily fast diffusion of the dimer for sufficiently weak noise. Moreover, upon application of a static bias force, the dimer exhibits a motion opposite to that force (absolute negative mobility). The key requirement for all these effects is a nonconvex interaction potential of the two particles.

关键词： MOLECULAR dynamics DIMERS SUBSTRATES (Materials science) BROKEN symmetry (Physics) nonconvex programming FORCE & energy

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nonconvexity of the relative entropy for Markov dynamics: A Fisher information approach

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Physical Review E 2013年第1期88卷 012112-012112页

作者： Matteo Polettini Massimiliano Esposito Complex Systems and Statistical Mechanics University of Luxembourg Campus Limpertsberg 162a Avenue de la Faïencerie L-1511 Luxembourg Grand Duchy of Luxembourg

We show via counterexamples that relative entropy between the solution of a Markovian master equation and the steady state is not a convex function of time. We thus disprove the hypotheses that a general evolution principle of thermodynamics based on the decrease of the nonadiabatic entropy production could hold. However, we argue that a large separation of typical decay times is necessary for nonconvex solutions to occur, making concave transients extremely short lived with respect to the main relaxation modes. We describe a general method based on the Fisher information matrix to discriminate between generators that admit nonconvex solutions and those that do not. While initial conditions leading to concave transients are shown to be extremely fine-tuned, by our method we are able to select nonconvex initial conditions that are arbitrarily close to the steady state. Convexity does occur when the system is close to satisfying detailed balance or, more generally, when certain normality conditions of the decay modes are satisfied. Our results circumscribe the range of validity of a conjecture by Maes et al. [Phys. Rev. Lett. 107, 010601 (2011)] regarding monotonicity of the large deviation rate functional for the occupation probability, showing that while the conjecture might hold in the long-time limit, the conditions for Lyapunov's second criterion for stability are not met.

关键词： nonconvex programming RELATIVITY (Physics) ENTROPY MARKOV processes FISHER information CONVEX functions THERMODYNAMICS

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