Proximal methods for nonlinear programming: double regularization and inexact subproblems

This paper describes the first phase of a project attempting to construct an efficient general-purpose nonlinear optimizer using an augmented Lagrangian outer loop with a relative error criterion, and an inner loop employing a state-of-the art conjugate gradient solver. The outer loop can also employ double regularized proximal kernels, a fairly recent theoretical development that leads to fully smooth subproblems. We first enhance the existing theory to show that our approach is globally convergent in both the primal and dual spaces when applied to convex problems. We then present an extensive computational evaluation using the CUTE test set, showing that some aspects of our approach are promising, but some are not. These conclusions in turn lead to additional computational experiments suggesting where to next focus our theoretical and computational efforts.

Applications of Linear Programming to Coding Theory

Maximum-likelihood decoding is often the optimal decoding rule one can use, but it is very costly to implement in a general setting. Much effort has therefore been dedicated to find efficient decoding algorithms that either achieve or approximate the error-correcting performance of the maximum-likelihood decoder. This dissertation examines two approaches to this problem. In 2003 Feldman and his collaborators defined the linear programming decoder, which operates by solving a linear programming relaxation of the maximum-likelihood decoding problem. As with many modern decoding algorithms, is possible for the linear programming decoder to output vectors that do not correspond to codewords; such vectors are known as pseudocodewords. In this work, we completely classify the set of linear programming pseudocodewords for the family of cycle codes. For the case of the binary symmetric channel, another approximation of maximum-likelihood decoding was introduced by Omura in 1972. This decoder employs an iterative algorithm whose behavior closely mimics that of the simplex algorithm. We generalize Omura's decoder to operate on any binary-input memoryless channel, thus obtaining a soft-decision decoding algorithm. Further, we prove that the probability of the generalized algorithm returning the maximum-likelihood codeword approaches 1 as the number of iterations goes to infinity.

Theoretical and implementation aspects in the mechanization of the metatheory of programming languages

Interactive theorem provers are tools designed for the certification of formal proofs developed by means of man-machine collaboration. Formal proofs obtained in this way cover a large variety of logical theories, ranging from the branches of mainstream mathematics, to the field of software verification. The border between these two worlds is marked by results in theoretical computer science and proofs related to the metatheory of programming languages. This last field, which is an obvious application of interactive theorem proving, poses nonetheless a serious challenge to the users of such tools, due both to the particularly structured way in which these proofs are constructed, and to difficulties related to the management of notions typical of programming languages like variable binding. This thesis is composed of two parts, discussing our experience in the development of the Matita interactive theorem prover and its use in the mechanization of the metatheory of programming languages. More specifically, part I covers: - the results of our effort in providing a better framework for the development of tactics for Matita, in order to make their implementation and debugging easier, also resulting in a much clearer code; - a discussion of the implementation of two tactics, providing infrastructure for the unification of constructor forms and the inversion of inductive predicates; we point out interactions between induction and inversion and provide an advancement over the state of the art. In the second part of the thesis, we focus on aspects related to the formalization of programming languages. We describe two works of ours: - a discussion of basic issues we encountered in our formalizations of part 1A of the Poplmark challenge, where we apply the extended inversion principles we implemented for Matita; - a formalization of an algebraic logical framework, posing more complex challenges, including multiple binding and a form of hereditary substitution; this work adopts, for the encoding of binding, an extension of Masahiko Sato's canonical locally named representation we designed during our visit to the Laboratory for Foundations of Computer Science at the University of Edinburgh, under the supervision of Randy Pollack.

SOMS: SurrOgate MultiStart algorithm for use with nonlinear programming for global optimization

SOMS is a general surrogate-based multistart algorithm, which is used in combination with any local optimizer to find global optima for computationally expensive functions with multiple local minima. SOMS differs from previous multistart methods in that a surrogate approximation is used by the multistart algorithm to help reduce the number of function evaluations necessary to identify the most promising points from which to start each nonlinear programming local search. SOMS’s numerical results are compared with four well-known methods, namely, Multi-Level Single Linkage (MLSL), MATLAB’s MultiStart, MATLAB’s GlobalSearch, and GLOBAL. In addition, we propose a class of wavy test functions that mimic the wavy nature of objective functions arising in many black-box simulations. Extensive comparisons of algorithms on the wavy testfunctions and on earlier standard global-optimization test functions are done for a total of 19 different test problems. The numerical results indicate that SOMS performs favorably in comparison to alternative methods and does especially well on wavy functions when the number of function evaluations allowed is limited.

A study of the effect of additional inequalities in integer programming for logical design.

Originally presented as the author's thesis (M.S.), University of Illinois at Urbana-Champaign.

Introduction to linear programming.

Mode of access: Internet.

A quest for helpful feedback to programming coursework

The 2011 National Student Survey (NSS) revealed that 40% of full-time students in England did not think that the feedback on their work has been helpful, even though 66% of these students agreed that the feedback was detailed and 62% of them agreed that the feedback has been prompt. Detailed feedback that is not considered helpful by students means a waste of tutors' time while students continue to struggle with their learning. What do students consider as helpful feedback? What are the qualities of helpful feedback? What are the preferred forms of feedback? How should tutors write feedback so that students will find it helpful? Can ICT help to improve the quality of feedback? In our ongoing search for answers to the above questions, we have trialled the use of a novel Internet application, called eCAF, to assess programming coursework from Engineering, Mathematics and Computing students and have collected their views on the feedback received through a survey. The survey reveals that most students prefer electronic feedback as given through eCAF, with verbal feedback ranked second and hand-written feedback ranked even lower. The survey also indicates that the feedback from some tutors is considered more helpful than others. We report on the detailed findings of the survey. By comparing the kinds of feedback given by each tutor who took part in the trial, we explore ways to improve the helpfulness of feedback on programming coursework in a bid to promote learning amongst engineering students.

A quest for helpful feedback to programming coursework

The 2011 National Student Survey (NSS) revealed that 40% of full-time students in England do not think that the feedback on their work has been helpful, even though 66% of these students agreed that the feedback was detailed and 62% of them agreed that the feedback has been prompt. Detailed feedback that is not considered helpful by students means a waste of tutors' time while students continue to struggle with their learning. What do students consider as helpful feedback? What are the qualities of helpful feedback? What are the preferred forms of feedback? How should tutors write feedback so that students will find it helpful? Can ICT help to improve the quality of feedback? In our ongoing search for answers to the above questions, we have trialled the use of a novel online application (eCAF) to assess programming coursework from engineering, mathematics and computing students and, through a survey, have collected their views on the feedback received. The survey reveals that most students prefer electronic feedback as given through eCAF, with verbal feedback ranked second and hand-written feedback ranked even lower. The survey also indicates that the feedback from some tutors is considered more helpful than others. We report on the detailed findings of the survey. By comparing the kinds of feedback given by each tutor who took part in the trial, we explore ways to improve the helpfulness of feedback on programming coursework in a bid to promote learning amongst engineering students.

Integer Programming Approach to HP Folding

One of the most widely studied protein structure prediction models is the hydrophobic-hydrophilic (HP) model, which explains the hydrophobic interaction and tries to maximize the number of contacts among hydrophobic amino-acids. In order to find a lower bound for the number of contacts, a number of heuristics have been proposed, but finding the optimal solution is still a challenge. In this research, we focus on creating a new integer programming model which is capable to provide tractable input for mixed-integer programming solvers, is general enough and allows relaxation with provable good upper bounds. Computational experiments using benchmark problems show that our formulation achieves these goals.

Method of Linear Programming as an Idea for High School Curriculum

2010 Mathematics Subject Classification: 97D40, 97M10, 97M40, 97N60, 97N80, 97R80

A Language for Compositional Programming: A Rationale and Design

Бойко Бл. Банчев - Представена е обосновка и описание на език за програмиране в композиционен стил за опитни и учебни цели. Под “композиционен” имаме предвид функционален стил на програмиране, при който пресмятането е йерархия от композиции и прилагания на функции. Един от данновите типове на езика е този на геометричните фигури, които могат да бъдат получавани чрез прости правила за съотнасяне и така също образуват йерархични композиции. Езикът е силно повлиян от GeomLab, но по редица свойства се различава от него значително. Статията разглежда основните черти на езика; подробното му описание и фигурноконструктивните му възможности ще бъдат представени в съпътстваща публикация.

A Software Platform for Teaching Programming with Grading Systems

Красимир Манев, Милослав Средков, Петър Армянов - Състезателните системи (СС) са незаменимо средство за организация на състезания по програмиране. Напоследък СС се използват и в обучението по програмиране. В статията е предложена платформа, която да интегрира възможностите на СС, създадени или използвани от авторите. Целта е изграждането на проста и ефективна среда за обучение по програмиране, подпомагаща учебния процес. Специфицирани са основните елементи на платформата, като резултат от предходно изследване, и една нейна възможна архитектура.

CORE: A Multi-Purpose Programming Contest Repository System

Яни Чаушев, Милослав Средков, Красимир Манев - Всяко състезание по програмиране използва множество софтуерни инструменти за управление на процесите по време на състезанието. Въпреки че тези инструменти обикновено покриват спецификите на конкретния вид състезание задоволително, те рядко адресират трудностите на дългосрочното съхранение на данни и оперативната съвместимост. В тази статия е представен един софтуерен инструмент адресиращ тези проблеми. Вместо комплексна система, касаеща всички аспекти на състезанието, CORE е централизирано хранилище за съхраняване и поддържане на необходимите за различни състезания данни. Представени са основните му елементи, текущото състояние на реализацията и перспективите за развитие на системата.

A Mixed Integer Quadratic Programming Model for the Low Autocorrelation Binary Sequence Problem

In this paper the low autocorrelation binary sequence problem (LABSP) is modeled as a mixed integer quadratic programming (MIQP) problem and proof of the model’s validity is given. Since the MIQP model is semidefinite, general optimization solvers can be used, and converge in a finite number of iterations. The experimental results show that IQP solvers, based on this MIQP formulation, are capable of optimally solving general/skew-symmetric LABSP instances of up to 30/51 elements in a moderate time. ACM Computing Classification System (1998): G.1.6, I.2.8.

Programming as Metacalculation

Report published in the Proceedings of the National Conference on "Education in the Information Society", Plovdiv, May, 2013