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Digital Predistortion for Power Amplifiers Using separable functions

IEEE TRANSACTIONS ON SIGNAL PROCESSING 2010年第8期58卷 4121-4130页

作者： Jiang, Hong Wilford, Paul A. Alcatel Lucent Bell Labs Murray Hill NJ 07974 USA

This paper is concerned with digital predistortion for linearization of RF high power amplifiers (HPAs). It has two objectives. First, we establish a theoretical framework for a generic predistorter system, and show that if a postdistorter exists, then it is also a predistorter, and therefore, the predistorter and postdistorter are equivalent. This justifies the indirect learning methods for a large class of HPAs. Second, we establish a systematic and general structure for a predistorter that is capable of compensating nonlinearity for a large variety of HPAs. This systematic structure is derived using approximation by separable functions, and avoids selection of predistorters based on the assumption of HPA models traditionally done in the literature.

关键词： Digital predistortion predistorter postdistorter power amplifier linearization separable functions

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Contraction Analysis of Monotone Systems via separable functions

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IEEE TRANSACTIONS ON AUTOMATIC CONTROL 2020年第8期65卷 3486-3501页

作者： Kawano, Yu Besselink, Bart Cao, Ming Hiroshima Univ Grad Sch Engn Higashihiroshima 7390046 Japan Univ Groningen Bernoulli Inst Math Comp Sci & Artificial Intelli NL-9700 AK Groningen Netherlands Univ Groningen Fac Sci & Engn NL-9700 AK Groningen Netherlands

In this paper, we study incremental stability of monotone nonlinear systems through contraction analysis. We provide sufficient conditions for incremental asymptotic stability in terms of the Lie derivatives of differential one-forms or Lie brackets of vector fields. These conditions can be viewed as sum- or max-separable conditions, respectively. For incremental exponential stability, we show that the existence of such separable functions is both necessary and sufficient under standard assumptions for the converse Lyapunov theorem of exponential stability. As a by-product, we also provide necessary and sufficient conditions for exponential stability of positive linear time-varying systems. The results are illustrated through examples.

关键词： Control theory Asymptotic stability Stability analysis Nonlinear systems Eigenvalues and eigenfunctions Linear systems Contraction analysis monotone systems nonlinear systems separable functions

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On interval branch-and-bound for additively separable functions with common variables

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JOURNAL OF GLOBAL OPTIMIZATION 2013年第3期56卷 1101-1121页

作者： Berenguel, J. L. Casado, L. G. Garcia, I. Hendrix, E. M. T. Messine, F. Univ Almeria TIC Supercomp Algorithms Res Grp 146 Almeria 04120 Spain Univ Almeria Dept Comp Architecture & Elect Almeria 04120 Spain Univ Malaga Dept Comp Architecture Malaga 29017 Spain Wageningen Univ NL-6700 AP Wageningen Netherlands Univ Toulouse ENSEEIHT IRIT UMR CNRS 5505 F-31000 Toulouse France

Interval branch-and-bound (B&B) algorithms are powerful methods which look for guaranteed solutions of global optimisation problems. The computational effort needed to reach this aim, increases exponentially with the problem dimension in the worst case. For separable functions this effort is less, as lower dimensional sub-problems can be solved individually. The question is how to design specific methods for cases where the objective function can be considered separable, but common variables occur in the sub-problems. This paper is devoted to establish the bases of B&B algorithms for separable problems. New B&B rules are presented based on derived properties to compute bounds. A numerical illustration is elaborated with a test-bed of problems mostly generated by combining traditional box constrained global optimisation problems, to show the potential of using the derived theoretical basis.

关键词： Branch-and-bound Interval arithmetic separable functions

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Convex envelopes of separable functions over regions defined by separable functions of the same type

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OPTIMIZATION LETTERS 2018年第8期12卷 1725-1739页

作者： Locatelli, Marco Univ Parma Dipartimento Ingn & Architettura Parco Area Sci 181-A I-43124 Parma Italy

In this paper we derive the convex envelope of separable functions obtained as a linear combination of strictly convex coercive one-dimensional functions over compact regions defined by linear combinations of the same one-dimensional functions. As a corollary of the main result, we are able to derive the convex envelope of any quadratic function (not necessarily separable) over any ellipsoid, and the convex envelope of some quadratic functions over a convex region defined by two quadratic constraints.

关键词： Convex envelopes separable functions Quadratic programming

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CHARACTERIZING THE NONDOMINATED SET BY separable functions

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JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS 1988年第3期59卷 423-444页

作者： HENIG, MI UNIV ILLINOIS URBANAIL 61801

We present sufficient and necessary conditions for classes of separable (additive) functions to generate the set of nondominated outcomes in multicriteria optimization problems. The basic technique consists of convexifying the set of outcomes and then applying the standard characterization of a convex set by a class of linear functions. The conditions include the case when the set of feasible alternatives is convex and the criteria are convex-transformable. We show that the sum of powers and the sum of functions of exponents can generate the nondominated set for an arbitrary set of outcomes (under compactness conditions). We also discuss monotonicity, proper nondominance, uniqueness and connectedness of solutions, and weights and trade-offs with respect to these functions.

关键词： Multicriteria optimization Pareto sets convex-transformable functions separable functions

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Spatiotemporal imaging with partially separable functions

Spatiotemporal imaging with partially separable functions

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4th IEEE International Symposium on Biomedical Imaging

作者： Liang, Zhi-Pei Univ Illinois Dept Elect & Comp Engn Urbana IL 61801 USA

ISBN: (纸本)9781424406715

Spatiotemporal imaging, including both dynamic imaging and spectroscopic imaging, has a wide range of applications from functional neuroimaging, cardiac imaging to metabolic cancer imaging. A practical challenge lies in obtaining high spatiotemporal resolution because the amount of data required increases exponentially as the physical dimension increases (curse of dimensionality). This paper describes a new way for spatiotemporal imaging using partially separable functions. This model admits highly sparse sampling of the data space, providing an effective way to achieve high spatiotemporal resolution. Practical imaging data will also be presented to demonstrate the performance of the new method.

关键词： spatiotemporal modeling Hilbert spaces separable functions tensor-product spaces

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Global Line Search Algorithm Hybridized with Quadratic Interpolation and Its Extension to separable functions 15

Global Line Search Algorithm Hybridized with Quadratic Inter...

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17th Genetic and Evolutionary Computation Conference (GECCO)

作者： Baudis, Petr Posik, Petr Czech Tech Univ Fac Elect Engn Dept Cybernet Tech 2 Prague 16627 6 Czech Republic

ISBN: (纸本)9781450334723

We propose a novel hybrid algorithm "Brent-STEP" for univariate global function minimization, based on the global line search method STEP and accelerated by Brent's method, a local optimizer that combines quadratic interpolation and golden section steps. We analyze the performance of the hybrid algorithm on various one-dimensional functions and experimentally demonstrate a significant improvement relative to its constituent algorithms in most cases. We then generalize the algorithm to multivariate functions, proposing a scheme to interleave evaluations across dimensions to achieve smoother and more efficient convergence. We experimentally demonstrate the highly competitive performance of the proposed multivariate algorithm on separable functions of the BBOB benchmark. The combination of good performance and smooth convergence on separable functions makes the algorithm an interesting candidate for inclusion in algorithmic portfolios or hybrid algorithms that aim to provide good performance on a wide range of problems.

关键词： Black-box optimization Line search separable functions Hybrid algorithm

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Multimodality and the Linkage-Learning Difficulty of Additive ly separable functions 14

Multimodality and the Linkage-Learning Difficulty of Additiv...

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16th Genetic and Evolutionary Computation Conference (GECCO)

作者： Martins, Jean Delbem, Alexandre C. B. Univ Sao Paulo Inst Math & Comp Sci BR-05508 Sao Paulo Brazil

ISBN: (纸本)9781450326629

Estimation of Distribution Algorithms (EDAs) have emerged from the synergy between machine-learning techniques and Genetic Algorithms (GAs). EDAs rely on probabilistic modeling for obtaining information about the underlying structure of optimization problems and implementing effective reproduction operators. The effectiveness of EDAs depends on the capacity of the model-building to extract reliable information about the problem. In this study we analyze additively separable functions and argue that the degree of multimodality of such functions defines their linkage-learning difficulty. Besides, by using entropy-based concepts and Jensen's inequality, we show how allelic pairwise independence may appear as a consequence of an increasing multimodality. The results characterize the linkage-learning difficulty of well-known functions, like the deceptive trap, bipolar and concatenated parity.

关键词： Linkage-learning Multimodality separable functions

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On the Separability of functions and Games

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IEEE TRANSACTIONS ON CONTROL OF NETWORK SYSTEMS 2024年第2期11卷 831-841页

作者： Arditti, Laura Como, Giacomo Fagnani, Fabio Politecn Torino Dept Math Sci GL Lagrange I-10129 Turin Italy Financial Sect Zurich Switzerland Lund Univ Dept Automat Control S-22100 Lund Sweden

We study the notion of (additive) separability of a function of several variables with respect to a hypergraph (H-graph). We prove the existence of a unique minimal H-graph with respect to which a function is separable and show that the corresponding minimal decomposition of the function can be obtained through a recursive algorithm. We then focus on (strategic form) games and propose a concept of separability for a game with respect to a forward directed hypergraph (FDH-graph). This notion refines and generalizes that of the graphical game and is invariant with respect to strategic equivalence. We show that every game is separable with respect to a minimal FDH-graph. Moreover, for exact potential games, such minimal FDH-graph reduces to the minimal H-graph of the potential function. Our results imply and refine known results on graphical potential games and yield a new proof of the celebrated Hammersely-Clifford theorem on Markov random fields.

关键词： Hammersley-Clifford theorem hypergraphical games network games potential games separable functions

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PRESERVATION OF CONVERGENCE OF CONVEX-SETS AND functions IN FINITE DIMENSIONS

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TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY 1981年第1期268卷 127-142页

作者： MCLINDEN, L BERGSTROM, RC UNIV PACIFIC DEPT MATHSTOCKTONCA 95211

Abstract: We study a convergence notion which has particular relevance for convex analysis and lends itself quite naturally to successive approximation schemes in a variety of areas. Motivated particularly by problems in optimization subject to constraints, we develop technical tools necessary for systematic use of this convergence in finite-dimensional settings. Simple conditions are established under which this convergence for sequences of sets, functions and subdifferentials is preserved under various basic operations, including, for example, those of addition and infimal convolution in the case of functions.

关键词： Successive approximation constrained optimization convergence convex analysis dual operations subdifferentials infimal convolution conjugate duality separable functions

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