Augmented Lagrangian method with nonmonotone penalty parameters for constrained optimization

At each outer iteration of standard Augmented Lagrangian methods one tries to solve a box-constrained optimization problem with some prescribed tolerance. In the continuous world, using exact arithmetic, this subproblem is always solvable. Therefore, the possibility of finishing the subproblem resolution without satisfying the theoretical stopping conditions is not contemplated in usual convergence theories. However, in practice, one might not be able to solve the subproblem up to the required precision. This may be due to different reasons. One of them is that the presence of an excessively large penalty parameter could impair the performance of the box-constraint optimization solver. In this paper a practical strategy for decreasing the penalty parameter in situations like the one mentioned above is proposed. More generally, the different decisions that may be taken when, in practice, one is not able to solve the Augmented Lagrangian subproblem will be discussed. As a result, an improved Augmented Lagrangian method is presented, which takes into account numerical difficulties in a satisfactory way, preserving suitable convergence theory. Numerical experiments are presented involving all the CUTEr collection test problems.

The boundedness of penalty parameters in an augmented Lagrangian method with constrained subproblems

Augmented Lagrangian methods are effective tools for solving large-scale nonlinear programming problems. At each outer iteration, a minimization subproblem with simple constraints, whose objective function depends on updated Lagrange multipliers and penalty parameters, is approximately solved. When the penalty parameter becomes very large, solving the subproblem becomes difficult; therefore, the effectiveness of this approach is associated with the boundedness of the penalty parameters. In this paper, it is proved that under more natural assumptions than the ones employed until now, penalty parameters are bounded. For proving the new boundedness result, the original algorithm has been slightly modified. Numerical consequences of the modifications are discussed and computational experiments are presented.

Visualization designs for constraint logic programming

We address the design and implementation of visual paradigms for observing the execution of constraint logic programs, aiming at debugging, tuning and optimization, and teaching. We focus on the display of data in CLP executions, where representation for constrained variables and for the constrains themselves are seeked. Two tools, VIFID and TRIFID, exemplifying the devised depictions, have been implemented, and are used to showcase the usefulness of the visualizations developed.

Stochastic dynamic programming for election timing: A game theory approach

In this paper, we consider dynamic programming for the election timing in the majoritarian parliamentary system such as in Australia, where the government has a constitutional right to call an early election. This right can give the government an advantage to remain in power for as long as possible by calling an election, when its popularity is high. On the other hand, the opposition's natural objective is to gain power, and it will apply controls termed as "boosts" to reduce the chance of the government being re-elected by introducing policy and economic responses. In this paper, we explore equilibrium solutions to the government, and the opposition strategies in a political game using stochastic dynamic programming. Results are given in terms of the expected remaining life in power, call and boost probabilities at each time at any level of popularity.

Cold nuclear matter effects on J/psi production as constrained by deuteron-gold measurements at root S(NN)=200 GeV

We present a new analysis of J/psi production yields in deuteron-gold collisions at root s(NN) =200 GeV using data taken from the PHENIX experiment in 2003 and previously published in S. S. Adler [Phys. Rev. Lett 96, 012304 (2006)]. The high statistics proton-proton J/psi data taken in 2005 are used to improve the baseline measurement and thus construct updated cold nuclear matter modification factors (R(dAu)). A suppression of J/psi in cold nuclear matter is observed as one goes forward in rapidity (in the deuteron-going direction), corresponding to a region more sensitive to initial-state low-x gluons in the gold nucleus. The measured nuclear modification factors are compared to theoretical calculations of nuclear shadowing to which a J/psi (or precursor) breakup cross section is added. Breakup cross sections of sigma(breakup)=2.8(-1.4)(+1.7) (2.2(-1.5)(+1.6)) mb are obtained by fitting these calculations to the data using two different models of nuclear shadowing. These breakup cross-section values are consistent within large uncertainties with the 4.2 +/- 0.5 mb determined at lower collision energies. Projecting this range of cold nuclear matter effects to copper-copper and gold-gold collisions reveals that the current constraints are not sufficient to firmly quantify the additional hot nuclear matter effect.

A STUDY OF PENALTY FORMULATIONS USED IN THE NUMERICAL APPROXIMATION OF A RADIALLY SYMMETRIC ELASTICITY PROBLEM

We consider a class of two-dimensional problems in classical linear elasticity for which material overlapping occurs in the absence of singularities. Of course, material overlapping is not physically realistic, and one possible way to prevent it uses a constrained minimization theory. In this theory, a minimization problem consists of minimizing the total potential energy of a linear elastic body subject to the constraint that the deformation field must be locally invertible. Here, we use an interior and an exterior penalty formulation of the minimization problem together with both a standard finite element method and classical nonlinear programming techniques to compute the minimizers. We compare both formulations by solving a plane problem numerically in the context of the constrained minimization theory. The problem has a closed-form solution, which is used to validate the numerical results. This solution is regular everywhere, including the boundary. In particular, we show numerical results which indicate that, for a fixed finite element mesh, the sequences of numerical solutions obtained with both the interior and the exterior penalty formulations converge to the same limit function as the penalization is enforced. This limit function yields an approximate deformation field to the plane problem that is locally invertible at all points in the domain. As the mesh is refined, this field converges to the exact solution of the plane problem.

Minimizing total tardiness in a stochastic single machine scheduling problem using approximate dynamic programming

This paper addresses the non-preemptive single machine scheduling problem to minimize total tardiness. We are interested in the online version of this problem, where orders arrive at the system at random times. Jobs have to be scheduled without knowledge of what jobs will come afterwards. The processing times and the due dates become known when the order is placed. The order release date occurs only at the beginning of periodic intervals. A customized approximate dynamic programming method is introduced for this problem. The authors also present numerical experiments that assess the reliability of the new approach and show that it performs better than a myopic policy.

ECONOMICAL OCCUPATION OF AGRICULTURAL AREA OF PIRACICABA (SAO PAULO STATE, BRAZIL), INCLUDING RISK THROUGH LINEAR PROGRAMMING

The economic occupation of an area of 500 ha for Piracicaba was studied with the irrigated cultures of maize, tomato, sugarcane and beans, having used models of deterministic linear programming and linear programming including risk for the Target-Motad model, where two situations had been analyzed. In the deterministic model the area was the restrictive factor and the water was not restrictive for none of the tested situations. For the first situation the gotten maximum income was of R$ 1,883,372.87 and for the second situation it was of R$ 1,821,772.40. In the model including risk a producer that accepts risk can in the first situation get the maximum income of R$ 1,883,372. 87 with a minimum risk of R$ 350 year(-1), and in the second situation R$ 1,821,772.40 with a minimum risk of R$ 40 year(-1). Already a producer averse to the risk can get in the first situation a maximum income of R$ 1,775,974.81 with null risk and for the second situation R$ 1.707.706, 26 with null risk, both without water restriction. These results stand out the importance of the inclusion of the risk in supplying alternative occupations to the producer, allowing to a producer taking of decision considered the risk aversion and the pretension of income.

Rough Notes on Programming AVR Microcontrollers in C

These notes follow on from the material that you studied in CSSE1000 Introduction to Computer Systems. There you studied details of logic gates, binary numbers and instruction set architectures using the Atmel AVR microcontroller family as an example. In your present course (METR2800 Team Project I), you need to get on to designing and building an application which will include such a microcontroller. These notes focus on programming an AVR microcontroller in C and provide a number of example programs to illustrate the use of some of the AVR peripheral devices.

Response (re-)programming in aging: A kinematic analysis

Background. Age-related motor slowing may reflect either motor programming deficits, poorer movement execution, or mere strategic preferences for online guidance of movement. We controlled such preferences, limiting the extent to which movements could be programmed. Methods. Twenty-four young and 24 older adults performed a line drawing task that allowed movements to he prepared in advance in one case (i.e., cue initially available indicating target location) and not in another (i.e., no cue initially available as to target location). Participants connected large or small targets illuminated by light-emitting diodes upon a graphics tablet that sampled pen tip position at 200 Hz. Results. Older adults had a disproportionate difficulty initiating movement when prevented from programming in advance. Older adults produced slower, less efficient movements, particularly when prevented from programming under greater precision requirements. Conclusions. The slower movements of older adults do not simply reflect a preference for online control, as older adults have less efficient movements when forced to reprogram their movements. Age-related motor slowing kinematically resembles that seen in patients with cerebellar dysfunction.

Small molecular probes for G-protein-coupled C5a receptors: Conformationally constrained antagonists derived from the C terminus of the human plasma protein C5a

Activation of the human complement system of plasma proteins in response to infection or injury produces a 4-helix bundle glycoprotein (74 amino acids) known as C5a. C5a binds to G-protein-coupled receptors on cell surfaces triggering receptor-ligand internalization, signal transduction, and powerful inflammatory responses. Since excessive levels of C5a are associated with autoimmune and chronic inflammatory disorders, inhibitors of receptor activation may have therapeutic potential. We now report solution structures and receptor-binding and antagonist activities for some of the first small molecule antagonists of C5a derived from its hexapeptide C terminus. The antagonist NMe-Phe-Lys-Pro-D-Cha-Trp-D-Arg-CO2H (1) surprisingly shows an unusually well-defined solution structure as determined by H-1 NMR spectroscopy. This is one of the smallest acyclic peptides found to possess a defined solution conformation, which can be explained by the constraining role of intramolecular hydrogen bonding. NOE and coupling constant data, slow deuterium exchange, and a low dependence on temperature for the chemical shift of the D-Cha-NH strongly indicate an inverse gamma turn stabilized by a D-Cha-NH ... OC-Lys hydrogen bond. Smaller conformational populations are associated with a hydrogen bond between Trp-NH ... OC-Lys, defining a type II beta turn distorted by the inverse gamma turn incorporated within it. An excellent correlation between receptor-affinity and antagonist activity is indicated for a limited set of synthetic peptides. Conversion of the C-terminal carboxylate of 1 to an amide decreases antagonist potency 5-fold, but potency is increased up to 10-fold over 1 if the amide bond is made between the C-terminal carboxylate and a Lys/Orn side chain to form a cyclic analogue. The solution structure of cycle 6 also shows gamma and beta turns; however, the latter occurs in a different position, and there are clear conformational changes in 6 vs 1 that result in enhanced activity. These results indicate that potent C5a antagonists can be developed by targeting site 2 alone of the C5a receptor and define a novel pharmacophore for developing powerful receptor probes or drug candidates.

The conserved quantity theory of causation and chance raising

In this paper I offer an 'integrating account' of singular causation, where the term 'integrating' refers to the following program for analysing causation. There are two intuitions about causation, both of which face serious counterexamples when used as the basis for an analysis of causation. The 'process' intuition, which says that causes and effects are linked by concrete processes, runs into trouble with cases of misconnections', where an event which serves to prevent another fails to do so on a particular occasion and yet the two events are linked by causal processes. The chance raising intuition, according to which causes raise the chance of their effects, easily accounts for misconnections but faces the problem of chance lowering causes, a problem easily accounted for by the process approach. The integrating program attempts to provide an analysis of singular causation by synthesising the two insights, so as to solve both problems. In this paper I show that extant versions of the integrating program due to Eells, Lewis, and Menzies fail to account for the chance-lowering counterexample. I offer a new diagnosis of the chance lowering case, and use that as a basis for an integrating account of causation which does solve both cases. In doing so, I accept various assumptions of the integrating program, in particular that there are no other problems with these two approaches. As an example of the process account, I focus on the recent CQ theory of Wesley Salmon (1997).

Programming internet based DAI applications in Qu-Prolog

This paper presents the unique collection of additional features of Qu-Prolog, a variant of the Al programming language Prolog, and illustrates how they can be used for implementing DAI applications. By this we mean applications comprising communicating information servers, expert systems, or agents, with sophisticated reasoning capabilities and internal concurrency. Such an application exploits the key features of Qu-Prolog: support for the programming of sound non-clausal inference systems, multi-threading, and high level inter-thread message communication between Qu-Prolog query threads anywhere on the internet. The inter-thread communication uses email style symbolic names for threads, allowing easy construction of distributed applications using public names for threads. How threads react to received messages is specified by a disjunction of reaction rules which the thread periodically executes. A communications API allows smooth integration of components written in C, which to Qu-Prolog, look like remote query threads.