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IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)

作者： Dumitrescu, Bogdan Sicleru, Bogdan C. Univ Politehn Bucuresti Dept Automat Control & Comp Bucharest 060042 Romania

ISBN: (纸本)9781479928934

We present a method for optimization with sums of exponentials subject to positivity constraints and apply it to the modeling of empirical probability distribution functions and to the design of IIR filters with non-negative impulse response. Our approach uses exponents in a sparse arithmetic progression and hence is able to transform the positivity condition to a polynomial form that is computationally tractable. We show how to obtain initial values for the exponents by sparsifying a full progression and then present an iterative optimization procedure using gradient steps. The modeling and design examples indicate a good behavior of our method.

关键词： convex optimization semi-infinite programming positive polynomials density modeling non-negative impulse response sparse arithmetic progression

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Local reduction based SQP-type method for semi-infinite programs with an infinite number of second-order cone constraints

Local reduction based SQP-type method for semi-infinite prog...

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25th European Conference on Operational Research (EURO)

作者： Okuno, Takayuki Fukushima, Masao Tokyo Univ Sci Div 1 Dept Management Sci Fac Engn Tokyo 1628601 Japan Nanzan Univ Fac Informat Syst & Engn Dept Informat Syst & Math Sci Nagoya Aichi 4890863 Japan

The second-order cone program (SOCP) is an optimization problem with second-order cone (SOC) constraints and has achieved notable developments in the last decade. The classical semi-infinite program (SIP) is represented with infinitely many inequality constraints, and has been studied extensively so far. In this paper, we consider the SIP with infinitely many SOC constraints, called the SISOCP for short. Compared with the standard SIP and SOCP, the studies on the SISOCP are scarce, even though it has important applications such as Chebychev approximation for vector-valued functions. For solving the SISOCP, we develop an algorithm that combines a local reduction method with an SQP-type method. In this method, we reduce the SISOCP to an SOCP with finitely many SOC constraints by means of implicit functions and apply an SQP-type method to the latter problem. We study the global and local convergence properties of the proposed algorithm. Finally, we observe the effectiveness of the algorithm through some numerical experiments.

关键词： semi-infinite programming Second-order cone constraints SQP-type method Local reduction method

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A reduction type penalty algorithm for nonlinear semi-infinite programming *

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IFAC Proceedings Volumes 2009年第2期42卷 40-45页

作者： Alzira Mota A. Ismael F. Vaz Institute Polytechnic of Porto Mathematic Department Engineering Institute Porto Portugal University of Minho Engineering School Production and Systems Department Portugal

semi-infinite programming (SIP) problems arise in several engineering areas such as, for example, robotic trajectory planning, production planning, digital filter design and air pollution control. In spite of being an active research area with many seminal works it lacks available software that could be used by the research community. The only exceptions are the fseminf MATLAB function, available in the Optimization Toolbox, and the NSIPS solver, but neither of them provide an implementation of a method belonging to the well known reduction type class. This paper proposes an implementation of a reduction type algorithm base on a penalty technique and provides a compare between several well known penalty functions. The provided numerical results with a significant number of SIP test problems are reported as performance profiles.

关键词： semi-infinite programming Reduction type algorithm Particle swarm optimization Penalty functions

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A nonmonotonic trust region algorithm for a class of semi-infinite minimax programming

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APPLIED MATHEMATICS AND COMPUTATION 2009年第2期215卷 474-480页

作者： Ou Yigui Zhou Qian Hainan Univ Dept Appl Math Haikou 570228 Peoples R China

Based on the discretization methods for solving semi-infinite programming problems, this paper presents a new nonmonotonic trust region algorithm for a class of semi-infinite minimax programming problem. Under some mild assumptions, the global convergence of the proposed algorithm is given. Numerical tests are reported that show the efficiency of the proposed method. (C) 2009 Elsevier Inc. All rights reserved.

关键词： semi-infinite programming Nonsmooth optimization Trust region algorithm Global convergence

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Quadratic programming Approach for UWB Pulse Shaping Filter Design with Nonconstant Upper Bounds

Quadratic Programming Approach for UWB Pulse Shaping Filter ...

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15th International Conference on Advanced Communications Technology (ICACT)

作者： Yusoff, Mohd Amaluddin Zang, Zhuquan Curtin Univ Dept Elect & Comp Engn Sarawak Malaysia

ISBN: (纸本)9788996865018;9781467331487

In UWB pulse shaping filter design, FIR filter formulated as a semi-definite programming problem has been widely used. Recently, piece-wise continuous bounds has been incorporated into the FIR filter design to avoid power loss due to the constant spectral mask indirectly assumed in the design. In this paper, we formulate the pulse shaping filter design as a semi-infinite quadratic optimization problem using Hermite-Rodriguez basis functions. Computationally effective approach to solving the optimization problem is proposed. Through numerical design examples, we compare the spectral utilization of our approach with those FIR-based pulse shaping filter designs. We demonstrate that our proposed approach is easy to implement and achieves better spectral utilization than a recent result when a suboptimal basic pulse is used.

关键词： pulse shaping filter design semi-infinite programming ultra-wideband (UWB) Hermite-Rodriguez functions

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An Iterative Technique for Optimally Designing Extrapolated Impulse Response Filter in the Mini-Max Sense

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IEICE TRANSACTIONS ON FUNDAMENTALS OF ELECTRONICS COMMUNICATIONS AND COMPUTER SCIENCES 2013年第10期E96A卷 2029-2033页

作者： Wang, Hao Zhao, Li Pei, Wenjiang Zuo, Jiakuo Wang, Qingyun Xin, Minghai Southeast Univ Sch Informat Sci & Engn Nanjing 210096 Peoples R China Southeast Univ Res Ctr Learning Sci Nanjing 210096 Jiangsu Peoples R China

The optimal design of an extrapolated impulse response (EIR) filter (in the mini-max sense) is a non-linear programming problem. In this paper, the optimal design of the EIR filter by the semi-infinite programming (SIP) is investigated and an iterative technique for optimally designing the EIR filter is proposed. The simulation experiment validates the effectiveness of the SIP technique and the proposed iterative technique in the optimal design of the EIR filter.

关键词： finite impulse response filter extrapolated impulse response filter principal component analysis semi-infinite programming linear programming

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Newsvendor optimization with limited distribution information

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OPTIMIZATION METHODS & SOFTWARE 2013年第3期28卷 640-667页

作者： Zhu, Zhisu Zhang, Jiawei Ye, Yinyu Oracle Corp Redwood Shores CA 94065 USA NYU Stern Sch Business IOMS OM New York NY 10012 USA Stanford Univ Dept Management Sci & Engn Stanford CA 94305 USA

Lack of complete distribution calls for stochastically robust models that, after exploiting available limited or partial information, offer risk-shielded solutions, or in other words, solutions that are insensitive to all possible distributions of random variables. We focus on the well-known newsvendor problem in this study, where the distribution of the random demand is only specified by its mean and one of the following: its standard deviation or its support. We propose a stochastically robust model for the newsvendor problem. More specifically, our model tries to minimize the regret that is defined as the ratio of the expected cost based on limited information to that based on complete information, called Relative Expected Value of Distribution (REVD). We show how to derive an optimal solution to the REVD model. Numerical examples are provided to compare our model with other similar approaches. The goal is to establish a confidence ratio that the decision from our model is not worse, relatively, too much than the decision based on the true distribution which would be never known exactly in real-world applications.

关键词： newsvendor regret semi-infinite programming linear fractional programming 90B05 90C34 90C32 90C15

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GENERATING MOMENT MATCHING SCENARIOS USING OPTIMIZATION TECHNIQUES

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SIAM JOURNAL ON OPTIMIZATION 2013年第2期23卷 963-999页

作者： Mehrotra, Sanjay Papp, David Northwestern Univ Dept Ind Engn & Management Sci Evanston IL 60208 USA

An optimization based method is proposed to generate moment matching scenarios for numerical integration and its use in stochastic programming. The main advantage of the method is its flexibility: it can generate scenarios matching any prescribed set of moments of the underlying distribution rather than matching all moments up to a certain order, and the distribution can be defined over an arbitrary set. This allows for a reduction in the number of scenarios and allows the scenarios to be better tailored to the problem at hand. The method is based on a semi-infinite linear programming formulation of the problem that is shown to be solvable with polynomial iteration complexity. A practical column generation method is implemented. The column generation subproblems are polynomial optimization problems;however, they need not be solved to optimality. It is found that the columns in the column generation approach can be efficiently generated by random sampling. The number of scenarios generated matches a lower bound of Tchakaloff's. The rate of convergence of the approximation error is established for continuous integrands, and an improved bound is given for smooth integrands. Extensive numerical experiments are presented in which variants of the proposed method are compared to Monte Carlo and quasi-Monte Carlo methods on both numerical integration problems and stochastic optimization problems. The benefits of being able to match any prescribed set of moments, rather than all moments up to a certain order, is also demonstrated using optimization problems with 100-dimensional random vectors. Empirical results show that the proposed approach outperforms Monte Carlo and quasi-Monte Carlo based approaches on the tested problems.

关键词： scenario generation moment matching cubature column generation convex programming statistical bounds semi-infinite programming

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Convexity and Variational Analysis 1

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Workshop on Computational and Analytical Mathematics

作者： Ioffe, A. D. Technion Israel Inst Technol Dept Math IL-32000 Haifa Israel

ISBN: (数字)9781461476214

ISBN: (纸本)9781461476214;9781461476207

The paper focuses on the interplay between methods of general variational analysis, on the one hand, and convex analysis, on the other (with a special emphasis on the efficiency of the latter), in treating problems that come from the general variational analysis when applied in substantial or virtual presence of convexity. We discuss a number of relating problems: error bounds, metric regularity, linear openness, and stability as well as first-order necessary optimality conditions in semi-infinite programming.

关键词： Distance to infeasibility Global error bound Linear openness and Lipschitz stability Metric regularity Perfect regularity semi-infinite programming Set-valued mapping

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THE ADAPTIVE CONVEXIFICATION ALGORITHM: A FEASIBLE POINT METHOD FOR semi-infinite programming

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SIAM JOURNAL ON OPTIMIZATION 2008年第4期18卷 1187-1208页

作者： Floudas, Christodoulos A. Stein, Oliver Univ Karlsruhe Sch Econ & Business Engn D-76128 Karlsruhe Germany Princeton Univ Dept Chem Engn Princeton NJ 08540 USA

We present a new numerical solution method for semi-infinite optimization problems. Its main idea is to adaptively construct convex relaxations of the lower level problem, replace the relaxed lower level problems equivalently by their Karush-Kuhn-Tucker conditions, and solve the resulting mathematical programs with complementarity constraints. This approximation produces feasible iterates for the original problem. The convex relaxations are constructed with ideas from the alpha BB method of global optimization. The necessary upper bounds for second derivatives of functions on box domains can be determined using the techniques of interval arithmetic, where our algorithm already works if only one such bound is available for the problem. We show convergence of stationary points of the approximating problems to a stationary point of the original semi-infinite problem within arbitrarily given tolerances. Numerical examples from Chebyshev approximation and design centering illustrate the performance of the method.

关键词： semi-infinite programming alpha BB global optimization convex optimization mathematical program with complementarity constraints bilevel optimization

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