Track routing optimizing timing and yield

Recently the authors have proposed a homogeneous and self-dual algorithm for solving the monotone complementarity problem (MCP) [5]. The algorithm is a single phase interior-point type method; nevertheless, it yields either an approximate optimal solution or detects a possible infeasibility of the problem. In this paper we specialize the algorithm to the solution of general smooth convex optimization problems, which also possess nonlinear inequality constraints and free variables. We discuss an implementation of the algorithm for large-scale sparse convex optimization. Moreover, we present computational results for solving quadratically constrained quadratic programming and geometric programming problems, where some of the problems contain more than 100,000 constraints and variables. The results indicate that the proposed algorithm is also practically efficient.

In this paper, we propose track routing and optimization for yield (TROY), the first track router for the optimization of yield loss due to random defects. As the probability of failure (POF), which is an integral of the critical area and the defect size distribution, strongly depends on wire ordering, sizing, and spacing, track routing can play a key role in effective wire planning for yield optimization. However, a straightforward formulation of yield-driven track routing can be shown to be integer nonlinear programming, which is a nondeterministic polynomial-time complete problem. TROY overcomes the computational complexity by combining two effective techniques, i.e., the minimum Hamiltonian path (MHP) from graph theory and the second-order cone programming (SOCP) from mathematical optimization. First, TROY performs wire ordering to minimize the critical area for short defects by finding an MHP. Then, TROY carries out optimal wire sizing/spacing through SOCP optimization based on the given wire order. Since the SOCP can be optimally solved in near linear time, TROY efficiently achieves globally optimal wire sizing/spacing for the minimal POF.

We consider a general multi-agent convex optimization problem where the agents are to collectively minimize a global objective function subject to a global inequality constraint, a global equality constraint, and a global constraint set. The objective function is defined by a sum of local objective functions, while the global constraint set is produced by the intersection of local constraint sets. In particular, we study two cases: one where the equality constraint is absent, and the other where the local constraint sets are identical. We devise two distributed primal-dual subgradient algorithms based on the characterization of the primal-dual optimal solutions as the saddle points of the Lagrangian and penalty functions. These algorithms can be implemented over networks with dynamically changing topologies but satisfying a standard connectivity property, and allow the agents to asymptotically agree on optimal solutions and optimal values of the optimization problem under the Slater's condition.

<p>In this thesis new robust methods for the efficient sharing of the radio spectrum for underlay cognitive radio (CR) systems are developed. These methods provide robustness against uncertainties in the channel state information (CSI) that is available to the cognitive radios. A stochastic approach is taken and the robust spectrum sharing methods are formulated as convex optimisation problems. Three efficient spectrum sharing methods; power control, cooperative beamforming and conventional beamforming are studied in detail. The CR power control problem is formulated as a sum rate maximisation problem and transformed into a convex optimisation problem. A robust power control method under the assumption of partial CSI is developed and also transformed into a convex optimisation problem. A novel method of detecting and removing infeasible constraints from the power allocation problem is presented that results in considerably improved performance. The performance of the proposed methods in Rayleigh fading channels is analysed by simulations. The concept of cooperative beamforming for spectrum sharing is applied to an underlay CR relay network. Distributed single antenna relay nodes are utilised to form a virtual antenna array that provides increased gains in capacity through cooperative beamforming. It is shown that the cooperative beamforming problems can be transformed into convex optimisation problems. New robust cooperative beamformers under the assumption of partial and imperfect CSI are developed and also transformed into convex optimisation problems. The performance of the proposed methods in Rayleigh fading channels is analysed by simulations. Conventional beamforming to allow efficient spectrum sharing in an underlay CR system is studied. The beamforming problems are formulated and transformed into convex optimisation problems. New robust beamformers under the assumption of partial and imperfect CSI are developed and also transformed into convex optimisation problems. The performance of the proposed methods in Rayleigh fading channels is analysed by simulations.</p>

Conventional methods for optimal sizing of wires and transistors use linear RC circuit models and the Elmore delay as a measure of signal delay. If the RC circuit has a tree topology the sizing problem reduces to a convex optimization problem which can be solved using geometric programming. The tree topology restriction precludes the use of these methods in several sizing problems of significant importance to high-performance deep submicron design including, for example, circuits with loops of resistors, e.g., clock distribution meshes, and circuits with coupling capacitors, e.g., buses with crosstalk between the lines. The paper proposes a new optimization method which can be used to address these problems. The method uses the dominant time constant as a measure of signal propagation delay in an RC circuit, instead of Elmore delay. Using this measure, sizing of any RC circuit can be cast as a convex optimization problem which can be solved using the recently developed efficient interior-point methods for semidefinite programming. The method is applied to two important sizing problems --- sizing of clock meshes, and sizing of buses in the presence of crosstalk.

We consider fusing an arbitrary number of multiband, i.e., panchromatic, multispectral, or hyperspectral, images of the same scene. Using the well-known forward observation and linear mixture models, a vector total-variation penalty, and appropriate constraints, we cast this problem as a convex optimization problem. The total-variation penalty helps cope with the potential ill-posedness of the underlying inverse problem by exploiting the prior knowledge that natural images are mostly piecewise smooth in the spatial domain and comprise relatively few archetypical signatures, i.e., endmembers, in the spectral domain. We solve the formulated convex but non-smooth optimization problem using the alternating direction method of multipliers. Our experiments with multiband images constructed from real hyperspectral datasets demonstrate the performance advantages of the proposed algorithm over the existing algorithms, which need to be used in tandem to fuse more than two multiband images.

Solving network flow problems is a fundamental component of traffic engineering and many communications applications, such as content delivery or multi-processor scheduling. While a rich body of work has addressed network flow problems in deterministic finding flows in where performance metrics like bandwidth and delay are uncertain and solely known by a probability distribution based on historical data, has received less attention. The work on stochastic networks has predominantly been directed to developing single-path routing algorithms, instead of addressing multi-path routing or flow problems. In this paper, we study constrained maximum flow problems in stochastic networks, where the delay and bandwidth of links are assumed to follow a log-concave probability distribution, which is the case for many distributions that could represent bandwidth and delay. We formulate the maximum-flow problem in such stochastic networks as a convex optimization problem, with a polynomial (in the input) number of variables. When an additional delay constraint is imposed, we show that the problem becomes NP-hard and we propose an approximation algorithm based on convex optimization. Furthermore, we develop a fast heuristic algorithm that, with a tuning parameter, is able to balance accuracy and speed. In a simulation-based evaluation of our algorithms in terms of success ratio, flow values, and running time, our heuristic is shown to give good results in a short running time.

Inexact alternating direction multiplier methods (ADMMs) are developed for solving general separable convex optimization problems with a linear constraint and with an objective that is the sum of smooth and nonsmooth terms. The approach involves linearized subproblems, a back substitution step, and either gradient or accelerated gradient techniques. Global convergence is established. The methods are particularly useful when the ADMM subproblems do not have closed form solution or when the solution of the subproblems is expensive. Numerical experiments based on image reconstruction problems show the effectiveness of the proposed methods.

We consider a general worst-case robust convex optimization problem, with arbitrary dependence on the uncertain parameters, which are assumed to lie in some given set of possible values. We describe a general method for solving such a problem, which alternates between optimization and worst-case analysis. With exact worst-case analysis, the method is shown to converge to a robust optimal point. With approximate worst-case analysis, which is the best we can do in many practical cases, the method seems to work very well in practice, subject to the errors in our worst-case analysis. We give variations on the basic method that can give enhanced convergence, reduce data storage, or improve other algorithm properties. Numerical simulations suggest that the method finds a quite robust solution within a few tens of steps; using warm-start techniques in the optimization steps reduces the overall effort to a modest multiple of solving a nominal problem, ignoring the parameter variation. The method is illustrated with several application examples.

Now the information system of the iron and steel industry is a typical sensor cloud computing system. The system has accumulated a lot of relevant manufacturing data. Using these data can well solve the slab storage problem in the production process for the iron and steel industry. In this paper, we investigate a queueing system where customers arrive according to a Markov Modulated Poisson Process (MMPP). MMPP can describe how the arrival rate changes with the environment, which is more realistic. We develop an MMPP(3)/M/C queueing model to solve the congestion problem in the iron and steel industry. In the actual production process, the slab arrival rates vary with states, therefore MMPP is used to model the arrival process in this paper. Based on explicit performance measures, we develop a nonlinear optimization model of queueing system, and convert the model into a convex optimization problem. Through the convex optimization method, the MMPP(3)/M/C model, resulted from the practical system, can be analyzed by the M/M/C model approximately.

The concept of a jump system, introduced by Bouchet and Cunningham [SIAM J. Discrete Math., 8 (1995), pp. 17–32], is a set of integer points with a certain exchange property. In this paper, we discuss several linear and convex optimization problems on jump systems and show that these problems can be solved in polynomial time under the assumption that a membership oracle for a jump system is available. We first present a polynomial-time implementation of the greedy algorithm for the minimization of a linear function. We then consider the minimization of a separable-convex function on a jump system and propose the first polynomial-time algorithm for this problem. The algorithm is based on the domain reduction approach developed in Shioura [Discrete Appl. Math., 84 (1998), pp. 215–220]. We finally consider the concept of M-convex functions on constant-parity jump systems which has been recently proposed by Murota [SIAM J. Discrete Math., 20 (2006), pp. 213–226]. It is shown that the minimization of an M-convex function can be solved in polynomial time by the domain reduction approach.

Synthesis of a non dispersive solvent extraction plant for effluent treatment and metal recovery

Convex optimization problems arise frequently in many different fields. This book provides a comprehensive introduction to the subject, and shows in detail how such problems can be solved numerically with great efficiency. The book begins with the basic elements of convex sets and functions, and then describes various classes of convex optimization problems. Duality and approximation techniques are then covered, as are statistical estimation techniques. Various geometrical problems are then presented, and there is detailed discussion of unconstrained and constrained minimization problems, and interior-point methods. The focus of the book is on recognizing convex optimization problems and then finding the most appropriate technique for solving them. It contains many worked examples and homework exercises and will appeal to students, researchers and practitioners in fields such as engineering, computer science, mathematics, statistics, finance and economics.

In this paper, we address the problem of QoS (Quality of Service) provisioning for multi-user video streaming over multiple heterogeneous wireless networks based on the distributed, cross-layer design framework. By jointly considering the rate allocation and the Joint Source-Channel Coding (JSCC), our proposal aims at maximizing the QoS provisioning under the given resource constraint. At first, we develop and evaluate a framework for optimal video rate allocation over multiple networks based on the observed Available Bit Rate (ABR) and the Round Trip Time (RTT) over each access network, as well as the video rate-distortion characteristics. The rate allocation is formulated as a convex optimization problem that minimizes the sum of all video streams expected distortion. Then, we propose an analytical JSCC scheme for error-resilient scalable encoded video, and integrate the JSCC with the specific rate allocation algorithm to improve the constructed video quality by optimally applying the appropriate channel coding rate given the constraints imposed by the transmission rate and the prevailing channel conditions. Objective and subjective simulation results are provided which demonstrate the effectiveness of our proposed joint scheme.

In this paper, a computational approach for controller design for polynomial systems with input constraints is proposed. The design is formulated as a convex optimization problem and capable of dealing with asymmetric input constraints. The idea of the method is to combine the recently introduced notion of virtual inputs and the notion of feedback passivity to obtain an optimization problem with polynomial constraints. The optimization problem is relaxed using the method of sum of squares which finally results in an LMI problem. The resulting state feedback controllers are non-polynomial. The approach contains some conservatism arising when formulating the design as a convex optimization problem. The introduction of slack variables and a postprocessing step reduces this conservatism. The applicability of the method is demonstrated by a controller design for a jet engine compressor.