Nonlinear Convex Optimization Problem Research Articles

Primal-dual potential reduction algorithm for symmetric programming problems with nonlinear objective functions

We consider a primal-dual potential reduction algorithm for nonlinear convex optimization problems over symmetric cones. The same complexity estimates as in the case of the linear objective function are obtained provided a certain nonlinear system of equations can be solved with a given accuracy. This generalizes the result of K. Kortanek, F. Potra and Y. Ye [7]. We further introduce a generalized Nesterov–Todd direction and show how it can be used to achieve a required accuracy (by solving the linearization of above mentioned nonlinear system) for a class of nonlinear convex functions satisfying scaling Lipschitz condition. This result is a far-reaching generalization of results of F. Potra, Y. Ye and J. Zhu [8], [9]. Finally, we show that a class of functions (which contains quantum entropy function) satisfies scaling Lipschitz condition.

A Sparsity-Based Regularization Approach for Deconvolution of Full-Waveform Airborne Lidar Data

Full-waveform lidar systems capture the complete backscattered signal from the interaction of the laser beam with targets located within the laser footprint. The resulting data have advantages over discrete return lidar, including higher accuracy of the range measurements and the possibility of retrieving additional returns from weak and overlapping pulses. In addition, radiometric characteristics of targets, e.g., target cross-section, can also be retrieved from the waveforms. However, waveform restoration and removal of the effect of the emitted system pulse from the returned waveform are critical for precise range measurement, 3D reconstruction and target cross-section extraction. In this paper, a sparsity-constrained regularization approach for deconvolution of the returned lidar waveform and restoration of the target cross-section is presented. Primal-dual interior point methods are exploited to solve the resulting nonlinear convex optimization problem. The optimal regularization parameter is determined based on the L-curve method, which provides high consistency in varied conditions. Quantitative evaluation and visual assessment of results show the superior performance of the proposed regularization approach in both removal of the effect of the system waveform and reconstruction of the target cross-section as compared to other prominent deconvolution approaches. This demonstrates the potential of the proposed approach for improving the accuracy of both range measurements and geophysical attribute retrieval. The feasibility and consistency of the presented approach in the processing of a variety of lidar data acquired under different system configurations is also highlighted.

Alocação de Potência Baseada na Margem de Certeza Equivalente Aplicável a Sistemas sem Fio Limitados por Interferência

<div class="page" title="Page 1"><div class="layoutArea"><div class="column"><div class="page" title="Page 1"><div class="layoutArea"><div class="column"><p>Neste artigo analisa-se o método de alocação de potência para redes de comunicação sem fio, limitadas em interferência de múltiplo acesso e com desvanecimento Rayleigh. O método leva em consideração a variação estatística da potência do sinal desejado e dos sinais interferentes e aloca ótima e dinamicamente os recursos de potência disponíveis no sistema. Esta alocação é feita levando-se em consideração as restrições impostas pela probabilidade de ocorrer falha na comunicação (interrupção) para cada par transmissor/receptor. Baseados na teoria de autovalor de Perron-Frobenius e na teoria de programação geométrica (GP), foram encontrados alguns resultados para o problema de otimização em questão. Um GP é um tipo especial de problema de otimização que pode ser transformado em um problema de otimização não linear convexo pela mudança de variáveis e assim ser resolvido globalmente. Também foi apresentado um método iterativo de rápida convergência para encontrar a alocação de potência ótima visando minimizar a probabilidade de falha na comunicação.</p></div></div></div></div></div></div>

A Joint Multitarget Estimator for the Joint Target Detection and Tracking Filter

Abstract : This paper proposes a joint multitarget (JoM) estimator for the joint target detection and tracking (JoTT) filter. An efficient choice to the unknown JoM estimation constant (i.e., hypervolume around target state estimate) is proposed as a Pareto-optimal solution to a multi-objective nonlinear convex optimization problem. The multi-objective function is formulated as two convex objective functions in conflict. The first objective function is the information theoretic part of the problem and aims for entropy maximization, while the second one arises from the constraint in the definition of the JoM estimator and aims to improve the accuracy of the JoM estimates. The Pareto-optimal solution is obtained using the weighted sum method, where objective weights are determined as linear predictions from autoregressive models. In contrast to the marginal multitarget (MaM) estimator, the target-present decision from the JoM estimator depends on the spatial information as well as the cardinality information in the finite-set statistics (FISST) density. The simulation results demonstrate that the JoM estimator achieves better track management performance in terms of track confirmation latency and track maintenance than the MaM estimator for different values of detection probability. However, the proposed JoM estimator suffers from track termination latency more than the MaM estimator since the localization performance of the JoTT filter does deteriorate gradually after target termination.

Novel Interior Point Algorithms for Solving Nonlinear Convex Optimization Problems

This paper proposes three numerical algorithms based on Karmarkar’s interior point technique for solving nonlinear convex programming problems subject to linear constraints. The first algorithm uses the Karmarkar idea and linearization of the objective function. The second and third algorithms are modification of the first algorithm using the Schrijver and Malek-Naseri approaches, respectively. These three novel schemes are tested against the algorithm of Kebiche-Keraghel-Yassine (KKY). It is shown that these three novel algorithms are more efficient and converge to the correct optimal solution, while the KKY algorithm fails in some cases. Numerical results are given to illustrate the performance of the proposed algorithms.

A starting-point strategy for interior-point algorithms for shakedown analysis of engineering structures

Lower-bound shakedown analysis leads to nonlinear convex optimization problems with large numbers of unknowns and constraints, the solution of which can be obtained efficiently by interior-point algorithms. The performance of these algorithms strongly depends on the choice of the starting point. In general, starting points should be located inside the feasible region. In addition, they should also be well centred. Although there exist several heuristics for the construction of suitable starting points, these are restricted, as long as only the mathematical procedure is considered without taking into account the nature of the underlying mechanical problem. Thus, in this article, a strategy is proposed for choosing appropriate starting points for interior-point algorithms applied to shakedown analysis. This strategy is based on both the mathematical characteristics and the physical meaning of the variables involved. The efficiency of the new method is illustrated by numerical examples from the field of power plant engineering.

Performance analysis and power allocation for multi-hop multi-branch amplify-and-forward cooperative networks over generalized fading channels

In this article, efficient power allocation strategies for multi-hop multi-branch amplify-and-forward networks are developed in generalized fading environments. In particular, we consider the following power optimization schemes: (i) minimizing of the all transmission powers subject to an outage constraint; and (ii) minimizing the outage probability subject to constraint on total transmit powers. In this study, we first derive asymptotically tight approximations for the statistics of the received signal-to-noise ratio (SNR) in the system under study with maximal ratio combining and selection combining receiver. With the statistical characterization of the received SNR, we then carry out a thorough performance analysis of the system. Finally, the asymptotic expression of the outage probability is used to formulate the original optimization problems using geometric programming (GP). The GP can readily be transformed into nonlinear convex optimization problem and therefore solved efficiently and globally using the interior-point methods. Numerical results are provided to substantiate the analytical results and to demonstrate the considerable performance improvement achieved by the power allocation.

A selective strategy for shakedown analysis of engineering structures

SUMMARYDetermining the load‐bearing capacity of engineering structures is essential for their design. In the case of varying thermo‐mechanical loading beyond the elastic limit, the statical shakedown analysis constitutes a particularly suitable tool for this. The application of the statical shakedown theorem, however, leads to a nonlinear convex optimization problem, which is typically characterized by large numbers of variables and constraints. In the present work, this optimization problem is solved by a primal–dual interior‐point algorithm, which shows a remarkable performance due to its problem‐tailored formulation. Nevertheless, the solution procedure remains still a demanding task from computational point of view. Thus, the aim of this paper is to tackle the task of solving large‐scale problems by use of a new so‐called selective algorithm. This algorithm detects automatically the plastically most affected zones within the structure, which have the highest influence on the solution. The entire system is then reduced to a substructure consisting of these zones, based upon which a new optimization problem can be set up, which is solved with significantly less effort. Consequently, the running time decreases drastically, as is shown by application to numerical examples from the field of power plant engineering. Copyright © 2013 John Wiley & Sons, Ltd.

Optimal BER-Balanced Combining for Weighted Energy Detection of UWB OOK Signals

For the demodulation of ultra-wideband (UWB) on-off keying (OOK) signals, some weighted energy detection (WED) schemes have been proposed. However, the schemes available suffer from unbalanced bit error rates (BERs) for bits "0" and "1". Therefore, in this letter we will address the optimal BER-balanced WED. Specifically, we incorporate the BER balance requirement into the WED formulation and obtain the optimal weighting vector by solving a nonlinear convex optimization problem. To bypass the computational complexity required by the convex optimization, we derive a simple but near-optimal weighting vector. Simulations illustrate that the proposed BER-balanced WED schemes can achieve almost the same BER performance as the maximum likelihood (ML) demodulator, which is optimal in terms of BER performance but produces unbalanced BERs for different bits.

Exponential penalty function formulation for multilevel optimization using the analytical target cascading framework

An exponential penalty function (EPF) formulation based on method of multipliers is presented for solving multilevel optimization problems within the framework of analytical target cascading. The original all-at-once constrained optimization problem is decomposed into a hierarchical system with consistency constraints enforcing the target-response coupling in the connected elements. The objective function is combined with the consistency constraints in each element to formulate an augmented Lagrangian with EPF. The EPF formulation is implemented using double-loop (EPF I) and single-loop (EPF II) coordination strategies and two penalty-parameter-updating schemes. Four benchmark problems representing nonlinear convex and non-convex optimization problems with different number of design variables and design constraints are used to evaluate the computational characteristics of the proposed approaches. The same problems are also solved using four other approaches suggested in the literature, and the overall computational efficiency characteristics are compared and discussed.

Solving general convex nonlinear optimization problems by an efficient neurodynamic model

In this paper, a neural network model is constructed on the basis of the duality theory, optimization theory, convex analysis theory, Lyapunov stability theory and LaSalle invariance principle to solve general convex nonlinear programming (GCNLP) problems. Based on the Saddle point theorem, the equilibrium point of the proposed neural network is proved to be equivalent to the optimal solution of the GCNLP problem. By employing Lyapunov function approach, it is also shown that the proposed neural network model is stable in the sense of Lyapunov and it is globally convergent to an exact optimal solution of the original problem. The simulation results also show that the proposed neural network is feasible and efficient.

A new subspace correction method for nonlinear unconstrained convex optimization problems

This paper gives a new subspace correction algorithm for nonlinear unconstrained convex optimization problems based on the multigrid approach proposed by S. Nash in 2000 and the subspace correction algorithm proposed by X. Tai and J. Xu in 2001. Under some reasonable assumptions, we obtain the convergence as well as a convergence rate estimate for the algorithm. Numerical results show that the algorithm is effective.

Shakedown analysis of engineering structures with limited kinematical hardening

We present a numerical method for the computation of shakedown loads of engineering structures with limited kinematical hardening under thermo-mechanical loading. The method is based on Melan’s statical shakedown theorem, which results in a nonlinear convex optimization problem. This is solved by an interior-point algorithm recently developed by the authors, specially designed for lower bound shakedown analysis of large-scale problems. Limited kinematical hardening is taken into account by use of a two-surface model, such that both alternating plasticity and incremental collapse can be captured. For the yield surface as well as for the bounding surface the von Mises criterion is used. The proposed method is validated by two examples, where numerical results are compared to those of literature where available.

Starting‐point strategy for interior‐point algorithms for lower‐bound shakedown analysis

AbstractShakedown analysis by using the lower‐bound theorem leads to computationally intensive nonlinear convex optimization problems with a large number of unknowns and constraints. Interior‐point algorithms such as recently developed by the authors have proven to be efficient for the solution of these problems. For convergence and efficiency of the iterative process of these algorithms the choice of the starting‐point is crucial. It should be inside of the feasible region and well‐centered for fast convergence.No general method exists for the construction of optimum starting‐points and only few investigations have been published on this issue. In this paper the physical meaning of the involved variables in shakedown problems is used to optimize starting‐points. The efficiency of the new method is illustrated by a numerical examples and comparison with an alternative approach. (© 2011 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Shakedown analysis with multidimensional loading spaces

A numerical method for the computation of shakedown loads of structures subjected to varying thermal and mechanical loading is proposed for the case of multidimensional loading spaces. The shakedown loading factors are determined based on the lower bound direct method using the von Mises yield criterion. The resulting nonlinear convex optimization problem is solved by use of the interior-point method. Although the underlying theory allows for the consideration of arbitrary numbers of loadings in principle, until now applications have been restricted to special cases, where either one or two loads vary independently. In this article, former formulations of the optimization problem are generalized for the case of arbitrary numbers of loadings. The method is implemented into an interior-point algorithm specially designed for this method. For illustration, numerical results are presented for a three-dimensional loading space applied to a square plate with a central circular hole.

A dynamic system model for solving convex nonlinear optimization problems

This paper proposes a feedback neural network model for solving convex nonlinear programming (CNLP) problems. Under the condition that the objective function is convex and all constraint functions are strictly convex or that the objective function is strictly convex and the constraint function is convex, the proposed neural network is proved to be stable in the sense of Lyapunov and globally convergent to an exact optimal solution of the original problem. The validity and transient behavior of the neural network are demonstrated by using some examples.

Three field finite elements for the elastoplastic analysis of 2D continua

A three field variational framework is used to formulate a new class of mixed finite elements for the elastoplastic analysis of 2D problems. The proposed finite elements are based on the independent interpolation of the stress, displacement and plastic multiplier fields. In particular new and richer interpolating patterns are proposed for the plastic multiplier in order to go beyond the oversimplifying constant assumption used in Bilotta and Casciaro (2007) [1]. As will be shown, this last choice is useful to simplify the return mapping algorithm but adversely affect the accuracy of the finite element. More articulated interpolations transform the return mapping process into a convex nonlinear optimization problem with few variables and constraints, a problem that can be efficiently solved using optimization algorithms, without penalizing overall computational efficiency. Several kinds of interpolations are proposed and compared with respect to accuracy and efficiency by performing a series of numerical tests on plane stress/strain problems modeled on the basis of the von Mises and Drucker–Prager yield functions. The reliability and good performance of the proposed elements are evident.

Numerical lower bound shakedown analysis of engineering structures

We propose a numerical method for the computation of shakedown loads of engineering structures subjected to varying thermo-mechanical loading. The method is based on Melan’s lower bound shakedown theorem using the von Mises yield criterion. The resulting nonlinear convex optimization problem is presented in a generalized formulation and then solved by an interior-point algorithm, which is characterized by a problem-tailored solution strategy, particularly suitable for application to large-scale engineering structures. Theoretical and numerical issues of the algorithm are described. It’s efficiency is shown by application to thermo-mechanical problems from power plant engineering. The results are compared to those found in literature as well as to calculations with other optimization codes lancelot, ipopt and ipdca.

Channel, capacity, and flow assignment in wireless mesh networks

We study the problem of channel capacity, and flow assignment (CCFA) in multi-channel wireless mesh networks (WMNs). CCFA involves the joint assignment of channels, distribution of wireless capacity, and determination of link flows to enhance the effectiveness of WMNs. We first study the capacity assignment (CA) problem in WMNs (WMN-CA) which involves the distribution of wireless capacity, given the topology and the flows (i.e., traffic demands and routing). Unlike wired networks, the capacities of different wireless links in a WMN have to be carved out of the capacities of wireless nodes. Since the wireless medium is shared by various wireless nodes, interference between different wireless links constrains the distribution of the wireless capacity available at individual nodes. We formulate WMN-CA as a convex non-linear optimization problem (NLP). We also present efficient heuristics to solve the problem and compare their relative performance. We then propose a linear programming (LP) based iterative algorithm for CCFA. We define a new metric, called network utility, which takes both throughput and average packet delay into account and includes a parameter that can be used to emphasize one over the other. Our approach has two separate phases – (1) channel assignment and (2) multi-channel capacity and flow assignment. The two phases of the iterative CCFA algorithm are performed repeatedly to improve the network utility which allows for a tradeoff between delay and throughput that can be achieved in a WMN.

Efficient recurrent neural network model for the solution of general nonlinear optimization problems

In this paper, we propose a projection neural network model for solving nonlinear convex optimization problems with general linear constraints. Compared with the existing neural network models for solving nonlinear optimization problems, the proposed neural network can be applied to solve a broad class of constrained optimization problems such as degenerate, saddle point, and quadratic problems. It is shown that the proposed neural network model is stable in the sense of Lyapunov and it is globally convergent. This model is exponentially stable. Simulation results are given to illustrate the global convergence and performance of the proposed model for various classes of constrained optimization problems. Both theoretical and numerical approaches are considered. Numerical results are in good agreement with the proved theoretical concepts.