988 resultados para Stochastic programming.


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We study the preconditioning of symmetric indefinite linear systems of equations that arise in interior point solution of linear optimization problems. The preconditioning method that we study exploits the block structure of the augmented matrix to design a similar block structure preconditioner to improve the spectral properties of the resulting preconditioned matrix so as to improve the convergence rate of the iterative solution of the system. We also propose a two-phase algorithm that takes advantage of the spectral properties of the transformed matrix to solve for the Newton directions in the interior-point method. Numerical experiments have been performed on some LP test problems in the NETLIB suite to demonstrate the potential of the preconditioning method discussed.

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We study four measures of problem instance behavior that might account for the observed differences in interior-point method (IPM) iterations when these methods are used to solve semidefinite programming (SDP) problem instances: (i) an aggregate geometry measure related to the primal and dual feasible regions (aspect ratios) and norms of the optimal solutions, (ii) the (Renegar-) condition measure C(d) of the data instance, (iii) a measure of the near-absence of strict complementarity of the optimal solution, and (iv) the level of degeneracy of the optimal solution. We compute these measures for the SDPLIB suite problem instances and measure the correlation between these measures and IPM iteration counts (solved using the software SDPT3) when the measures have finite values. Our conclusions are roughly as follows: the aggregate geometry measure is highly correlated with IPM iterations (CORR = 0.896), and is a very good predictor of IPM iterations, particularly for problem instances with solutions of small norm and aspect ratio. The condition measure C(d) is also correlated with IPM iterations, but less so than the aggregate geometry measure (CORR = 0.630). The near-absence of strict complementarity is weakly correlated with IPM iterations (CORR = 0.423). The level of degeneracy of the optimal solution is essentially uncorrelated with IPM iterations.

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These are the resources for an introductory lecture in JavaScript programming. Exercises are provided to practice simple JavaScript programming, including a template for a DHTML implementation of Conway's Game of Life (with encrypted solution).

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Exam questions and solutions for a third year mathematical programming course.

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Exercises, exams and solutions for a second year maths course.

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An overview of programming and software development.

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In this lecture we describe the structure of the Programming Principles course at Southampton, look at the definitions and paradigms of programming, and take a look ahead to the key things that we will be covering in the weeks ahead.

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In this lecture we look at key concepts in Java: how to write, compile and run Java programs, define a simple class, create a main method, and use if/else structures to define behaviour.

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In this session we look more closely at the way that Java deals with variables, and in particular with the differences between primitives (basic types like int and char) and objects. We also take an initial look at the scoping rules in Java, which dictate the visibility of variables in your program

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In this session we look at how to think systematically about a problem and create a solution. We look at the definition and characteristics of an algorithm, and see how through modularisation and decomposition we can then choose a set of methods to create. We also compare this somewhat procedural approach, with the way that design works in Object Oriented Systems,

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In this session we look at how to create more powerful objects through more powerful methods. We look at parameters and call by value vs. call by reference; return types; and overloading.

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In this session we look at the public and protected keywords, and the principle of encapsulation. We also look at how Constructors can help you initialise objects, while maintaining the encapsulation principle.

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In this session we look at the different types of loop in the Java language, and see how they can be used to iterate over Arrays.

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In this session we look at how we can use collection objects like ArrayList as a more advanced type of array. We also introduce the idea of generics (forcing a collection to hold a particular type) and see how Java handles the autoboxing and unboxing of primitives. Finally we look at Iterators, a common design pattern for dealing with iteration over a collection.

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In this session we point you at the Java Library, and go into some more details on how Strings work. We also introduce the HashMap class (a very useful type of collection).