Global ETD Search

1	Convergence Analysis of Generalized Primal-Dual Interior-Point Algorithms for Linear Optimization Wei, Hua January 2002 (has links) We study the zeroth-, first-, and second-order algorithms proposed by Tuncel. The zeroth-order algorithms are the generalization of the classic primal-dual affine-scaling methods, and have a strong connection with the quasi-Newton method. Although the zeroth-order algorithms have the property of strict monotone decrease in both primal and dual objective values, they may not converge. We give an illustrative example as well as an algebraic proof to show that the zeroth-order algorithms do not converge to an optimal solution in some cases. The second-order algorithms use the gradients and Hessians of the barrier functions. Tuncel has shown that all second-order algorithms have a polynomial iteration bound. The second-order algorithms have a range of primal-dual scaling matrices to be chosen. We give a method to construct such a primal-dual scaling matrix. We then analyze a new centrality measure. This centrality measure appeared in both first- and second-order algorithms. We compare the neighbourhood defined by this centrality measure with other known neighbourhoods. We then analyze how this centrality measure changes in the next iteration in terms of the step length and some other information of the current iteration. Mathematics Primal-dual interior-point methods Linear Optimization Convergence Polynomial algorithm
2	Convergence Analysis of Generalized Primal-Dual Interior-Point Algorithms for Linear Optimization Wei, Hua January 2002 (has links) We study the zeroth-, first-, and second-order algorithms proposed by Tuncel. The zeroth-order algorithms are the generalization of the classic primal-dual affine-scaling methods, and have a strong connection with the quasi-Newton method. Although the zeroth-order algorithms have the property of strict monotone decrease in both primal and dual objective values, they may not converge. We give an illustrative example as well as an algebraic proof to show that the zeroth-order algorithms do not converge to an optimal solution in some cases. The second-order algorithms use the gradients and Hessians of the barrier functions. Tuncel has shown that all second-order algorithms have a polynomial iteration bound. The second-order algorithms have a range of primal-dual scaling matrices to be chosen. We give a method to construct such a primal-dual scaling matrix. We then analyze a new centrality measure. This centrality measure appeared in both first- and second-order algorithms. We compare the neighbourhood defined by this centrality measure with other known neighbourhoods. We then analyze how this centrality measure changes in the next iteration in terms of the step length and some other information of the current iteration. Mathematics Primal-dual interior-point methods Linear Optimization Convergence Polynomial algorithm
3	Fast Methods for Bimolecular Charge Optimization Bardhan, Jaydeep P., Lee, J.H., Kuo, Shihhsien, Altman, Michael D., Tidor, Bruce, White, Jacob K. 01 1900 (has links) We report a Hessian-implicit optimization method to quickly solve the charge optimization problem over protein molecules: given a ligand and its complex with a receptor, determine the ligand charge distribution that minimizes the electrostatic free energy of binding. The new optimization couples boundary element method (BEM) and primal-dual interior point method (PDIPM); initial results suggest that the method scales much better than the previous methods. The quadratic objective function is the electrostatic free energy of binding where the Hessian matrix serves as an operator that maps the charge to the potential. The unknowns are the charge values at the charge points, and they are limited by equality and inequality constraints that model physical considerations, i.e. conservation of charge. In the previous approaches, finite-difference method is used to model the Hessian matrix, which requires significant computational effort to remove grid-based inaccuracies. In the novel approach, BEM is used instead, with precorrected FFT (pFFT) acceleration to compute the potential induced by the charges. This part will be explained in detail by Shihhsien Kuo in another talk. Even though the Hessian matrix can be calculated an order faster than the previous approaches, still it is quite expensive to find it explicitly. Instead, the KKT condition is solved by a PDIPM, and a Krylov based iterative solver is used to find the Newton direction at each step. Hence, only Hessian times a vector is necessary, which can be evaluated quickly using pFFT. The new method with proper preconditioning solves a 500 variable problem nearly 10 times faster than the techniques that must find a Hessian matrix explicitly. Furthermore, the algorithm scales nicely due to the robustness in number of IPM iterations to the size of the problem. The significant reduction in cost allows the analysis of much larger molecular system than those could be solved in a reasonable time using the previous methods. / Singapore-MIT Alliance (SMA) Hessian-implicit optimization bimolecular charge optimization boundary element method primal-dual interior point method Krylov based iterative solver
4	Studies on Optimization Methods for Nonlinear Semidefinite Programming Problems / 非線形半正定値計画問題に対する最適化手法の研究 Yamakawa, Yuya 23 March 2015 (has links) 京都大学 / 0048 / 新制・課程博士 / 博士(情報学) / 甲第19122号 / 情博第568号 / 新制\|\|情\|\|100(附属図書館) / 32073 / 京都大学大学院情報学研究科数理工学専攻 / (主査)教授山下信雄, 教授太田快人, 教授永持仁 / 学位規則第4条第1項該当 / Doctor of Informatics / Kyoto University / DFAM Optimization Nonlinear semidefinite programming Global convergence Superlinear convergence Primal-dual interior point method Block coordinate descent method 007
5	Market-based transmission congestion management using extended optimal power flow techniques Wang, Xing January 2001 (has links) This thesis describes research into the problem of transmission congestion management. The causes, remedies, pricing methods, and other issues of transmission congestion are briefly reviewed. This research is to develop market-based approaches to cope with transmission congestion in real-time, short-run and long-run efficiently, economically and fairly. Extended OPF techniques have been playing key roles in many aspects of electricity markets. The Primal-Dual Interior Point Linear Programming and Quadratic Programming are applied to solve various optimization problems of congestion management proposed in the thesis. A coordinated real-time optimal dispatch method for unbundled electricity markets is proposed for system balancing and congestion management. With this method, almost all the possible resources in different electricity markets, including operating reserves and bilateral transactions, can be used to eliminate the real-time congestion according to their bids into the balancing market. Spot pricing theory is applied to real-time congestion pricing. Under the same framework, a Lagrangian Relaxation based region decomposition OPF algorithm is presented to deal with the problems of real-time active power congestion management across multiple regions. The inter/intra-regional congestion can be relieved without exchanging any information between regional ISOs but the Lagrangian Multipliers. In day-ahead spot market, a new optimal dispatch method is proposed for congestion and price risk management, particularly for bilateral transaction curtailment. Individual revenue adequacy constraints, which include payments from financial instruments, are involved in the original dispatch problem. An iterative procedure is applied to solve this special optimization problem with both primal and dual variables involved in its constraints. An optimal Financial Transmission Rights (FTR) auction model is presented as an approach to the long-term congestion management. Two types of series F ACTS devices are incorporated into this auction problem using the Power Injection Model to maximize the auction revenue. Some new treatment has been done on TCSC's operating limits to keep the auction problem linear. 621.042
6	Evaluating the Benefits of Optimal Allocation of Wind Turbines for Distribution Network Operators Siano, P., Mokryani, Geev January 2015 (has links) No / This paper proposes a hybrid optimization method for optimal allocation of wind turbines (WTs) that combines a fast and elitist multiobjective genetic algorithm (MO-GA) and the market-based optimal power flow (OPF) to jointly minimize the total energy losses and maximize the net present value associated with the WT investment over a planning horizon. The method is conceived for distributed-generator-owning distribution network operators to find the optimal numbers and sizes of WTs among different potential combinations. MO-GA is used to select, among all the candidate buses, the optimal sites and sizes of WTs. A nondominated sorting GA II procedure is used for finding multiple Pareto-optimal solutions in a multiobjective optimization problem, while market-based OPF is used to simulate an electricity market session. The effectiveness of the method is demonstrated with an 84-bus 11.4-kV radial distribution system. Distribution network operator DNO Genetic algorithm GA Social welfare maximisation Wind turbines Optimal power-flow Interior-point method Distribution-systems Optimisation methods Genetic algorithm Generation Energy
7	A Multi-Factor Stock Market Model with Regime-Switches, Student's T Margins, and Copula Dependencies Berberovic, Adnan, Eriksson, Alexander January 2017 (has links) Investors constantly seek information that provides an edge over the market. One of the conventional methods is to find factors which can predict asset returns. In this study we improve the Fama and French Five-Factor model with Regime-Switches, student's t distributions and copula dependencies. We also add price momentum as a sixth factor and add a one-day lag to the factors. The Regime-Switches are obtained from a Hidden Markov Model with conditional Student's t distributions. For the return process we use factor data as input, Student's t distributed residuals, and Student's t copula dependencies. To fit the copulas, we develop a novel approach based on the Expectation-Maximisation algorithm. The results are promising as the quantiles for most of the portfolios show a good fit to the theoretical quantiles. Using a sophisticated Stochastic Programming model, we back-test the predictive power over a 26 year period out-of-sample. Furthermore we analyse the performance of different factors during different market regimes. finance statistics stock market stocks factor factors probability probability distribution students t distrbution students t copula markov chain hidden markov model regime switching stochastic programming optimisation optimization multi factor model arbitrage pricing theory return performance back test expectation maximisation expectation maximization multiple linear regression stochastic process primal-dual interior point qq-plot qq plot excess return market regimes bear market bull market market index index Probability Theory and Statistics Sannolikhetsteori och statistik

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