Direct-search penalty/barrier methods

In Nonlinear Optimization Penalty and Barrier Methods are normally used to solve Constrained Problems. There are several Penalty/Barrier Methods and they are used in several areas from Engineering to Economy, through Biology, Chemistry, Physics among others. In these areas it often appears Optimization Problems in which the involved functions (objective and constraints) are non-smooth and/or their derivatives are not know. In this work some Penalty/Barrier functions are tested and compared, using in the internal process, Derivative-free, namely Direct Search, methods. This work is a part of a bigger project involving the development of an Application Programming Interface, that implements several Optimization Methods, to be used in applications that need to solve constrained and/or unconstrained Nonlinear Optimization Problems. Besides the use of it in applied mathematics research it is also to be used in engineering software packages.

Derivative-free optimization and filter methods to solve nonlinear constrained problems

In real optimization problems, usually the analytical expression of the objective function is not known, nor its derivatives, or they are complex. In these cases it becomes essential to use optimization methods where the calculation of the derivatives, or the verification of their existence, is not necessary: the Direct Search Methods or Derivative-free Methods are one solution. When the problem has constraints, penalty functions are often used. Unfortunately the choice of the penalty parameters is, frequently, very difficult, because most strategies for choosing it are heuristics strategies. As an alternative to penalty function appeared the filter methods. A filter algorithm introduces a function that aggregates the constrained violations and constructs a biobjective problem. In this problem the step is accepted if it either reduces the objective function or the constrained violation. This implies that the filter methods are less parameter dependent than a penalty function. In this work, we present a new direct search method, based on simplex methods, for general constrained optimization that combines the features of the simplex method and filter methods. This method does not compute or approximate any derivatives, penalty constants or Lagrange multipliers. The basic idea of simplex filter algorithm is to construct an initial simplex and use the simplex to drive the search. We illustrate the behavior of our algorithm through some examples. The proposed methods were implemented in Java.

Classification of some penalty methods

Optimization problems arise in science, engineering, economy, etc. and we need to find the best solutions for each reality. The methods used to solve these problems depend on several factors, including the amount and type of accessible information, the available algorithms for solving them, and, obviously, the intrinsic characteristics of the problem. There are many kinds of optimization problems and, consequently, many kinds of methods to solve them. When the involved functions are nonlinear and their derivatives are not known or are very difficult to calculate, these methods are more rare. These kinds of functions are frequently called black box functions. To solve such problems without constraints (unconstrained optimization), we can use direct search methods. These methods do not require any derivatives or approximations of them. But when the problem has constraints (nonlinear programming problems) and, additionally, the constraint functions are black box functions, it is much more difficult to find the most appropriate method. Penalty methods can then be used. They transform the original problem into a sequence of other problems, derived from the initial, all without constraints. Then this sequence of problems (without constraints) can be solved using the methods available for unconstrained optimization. In this chapter, we present a classification of some of the existing penalty methods and describe some of their assumptions and limitations. These methods allow the solving of optimization problems with continuous, discrete, and mixing constraints, without requiring continuity, differentiability, or convexity. Thus, penalty methods can be used as the first step in the resolution of constrained problems, by means of methods that typically are used by unconstrained problems. We also discuss a new class of penalty methods for nonlinear optimization, which adjust the penalty parameter dynamically.

Filters method in direct search optimization, new measures to admissibility

Constrained nonlinear optimization problems are usually solved using penalty or barrier methods combined with unconstrained optimization methods. Another alternative used to solve constrained nonlinear optimization problems is the lters method. Filters method, introduced by Fletcher and Ley er in 2002, have been widely used in several areas of constrained nonlinear optimization. These methods treat optimization problem as bi-objective attempts to minimize the objective function and a continuous function that aggregates the constraint violation functions. Audet and Dennis have presented the rst lters method for derivative-free nonlinear programming, based on pattern search methods. Motivated by this work we have de- veloped a new direct search method, based on simplex methods, for general constrained optimization, that combines the features of the simplex method and lters method. This work presents a new variant of these methods which combines the lters method with other direct search methods and are proposed some alternatives to aggregate the constraint violation functions.

GLODS: Global and Local Optimization using Direct Search

Locating and identifying points as global minimizers is, in general, a hard and time-consuming task. Difficulties increase in the impossibility of using the derivatives of the functions defining the problem. In this work, we propose a new class of methods suited for global derivative-free constrained optimization. Using direct search of directional type, the algorithm alternates between a search step, where potentially good regions are located, and a poll step where the previously located promising regions are explored. This exploitation is made through the launching of several instances of directional direct searches, one in each of the regions of interest. Differently from a simple multistart strategy, direct searches will merge when sufficiently close. The goal is to end with as many direct searches as the number of local minimizers, which would easily allow locating the global extreme value. We describe the algorithmic structure considered, present the corresponding convergence analysis and report numerical results, showing that the proposed method is competitive with currently commonly used global derivative-free optimization solvers.

Parental Leave and Mothers' Careers: The Relative Importance of Job Protection and Cash Benefits

Job protection and cash benefits are key elements of parental leave (PL) systems. We study how these two policy instruments affect return-to-work and medium-run labour market outcomes of mothers of newborn children. Analysing a series of major PL policy changes in Austria, we find that longer cash benefits lead to a significant delay in return-to-work, particularly so in the period that is job-protected. Prolonged parental leave absence induced by these policy changes does not appear to hurt mothers' labour market outcomes in the medium run. We build a non-stationary model of job search after childbirth to isolate the role of the two policy instruments. The model matches return-to-work and return to same employer profiles under the various factual policy configurations. Counterfactual policy simulations indicate that a system that combines cash with protection dominates other systems in generating time for care immediately after birth while maintaining mothers' medium-run labour market attachment.

Towards Direct Policy Search Reinforcement Learning for Robot Control

This paper proposes a high-level reinforcement learning (RL) control system for solving the action selection problem of an autonomous robot. Although the dominant approach, when using RL, has been to apply value function based algorithms, the system here detailed is characterized by the use of direct policy search methods. Rather than approximating a value function, these methodologies approximate a policy using an independent function approximator with its own parameters, trying to maximize the future expected reward. The policy based algorithm presented in this paper is used for learning the internal state/action mapping of a behavior. In this preliminary work, we demonstrate its feasibility with simulated experiments using the underwater robot GARBI in a target reaching task

Evidence-based Economic Policy - Three Essays in Applied Microeconometrics

Over thirty years ago, Leamer (1983) - among many others - expressed doubts about the quality and usefulness of empirical analyses for the economic profession by stating that "hardly anyone takes data analyses seriously. Or perhaps more accurately, hardly anyone takes anyone else's data analyses seriously" (p.37). Improvements in data quality, more robust estimation methods and the evolution of better research designs seem to make that assertion no longer justifiable (see Angrist and Pischke (2010) for a recent response to Leamer's essay). The economic profes- sion and policy makers alike often rely on empirical evidence as a means to investigate policy relevant questions. The approach of using scientifically rigorous and systematic evidence to identify policies and programs that are capable of improving policy-relevant outcomes is known under the increasingly popular notion of evidence-based policy. Evidence-based economic policy often relies on randomized or quasi-natural experiments in order to identify causal effects of policies. These can require relatively strong assumptions or raise concerns of external validity. In the context of this thesis, potential concerns are for example endogeneity of policy reforms with respect to the business cycle in the first chapter, the trade-off between precision and bias in the regression-discontinuity setting in chapter 2 or non-representativeness of the sample due to self-selection in chapter 3. While the identification strategies are very useful to gain insights into the causal effects of specific policy questions, transforming the evidence into concrete policy conclusions can be challenging. Policy develop- ment should therefore rely on the systematic evidence of a whole body of research on a specific policy question rather than on a single analysis. In this sense, this thesis cannot and should not be viewed as a comprehensive analysis of specific policy issues but rather as a first step towards a better understanding of certain aspects of a policy question. The thesis applies new and innovative identification strategies to policy-relevant and topical questions in the fields of labor economics and behavioral environmental economics. Each chapter relies on a different identification strategy. In the first chapter, we employ a difference- in-differences approach to exploit the quasi-experimental change in the entitlement of the max- imum unemployment benefit duration to identify the medium-run effects of reduced benefit durations on post-unemployment outcomes. Shortening benefit duration carries a double- dividend: It generates fiscal benefits without deteriorating the quality of job-matches. On the contrary, shortened benefit durations improve medium-run earnings and employment possibly through containing the negative effects of skill depreciation or stigmatization. While the first chapter provides only indirect evidence on the underlying behavioral channels, in the second chapter I develop a novel approach that allows to learn about the relative impor- tance of the two key margins of job search - reservation wage choice and search effort. In the framework of a standard non-stationary job search model, I show how the exit rate from un- employment can be decomposed in a way that is informative on reservation wage movements over the unemployment spell. The empirical analysis relies on a sharp discontinuity in unem- ployment benefit entitlement, which can be exploited in a regression-discontinuity approach to identify the effects of extended benefit durations on unemployment and survivor functions. I find evidence that calls for an important role of reservation wage choices for job search be- havior. This can have direct implications for the optimal design of unemployment insurance policies. The third chapter - while thematically detached from the other chapters - addresses one of the major policy challenges of the 21st century: climate change and resource consumption. Many governments have recently put energy efficiency on top of their agendas. While pricing instru- ments aimed at regulating the energy demand have often been found to be short-lived and difficult to enforce politically, the focus of energy conservation programs has shifted towards behavioral approaches - such as provision of information or social norm feedback. The third chapter describes a randomized controlled field experiment in which we discuss the effective- ness of different types of feedback on residential electricity consumption. We find that detailed and real-time feedback caused persistent electricity reductions on the order of 3 to 5 % of daily electricity consumption. Also social norm information can generate substantial electricity sav- ings when designed appropriately. The findings suggest that behavioral approaches constitute effective and relatively cheap way of improving residential energy-efficiency.

Unemployment insurance with endogenous search intensity and precautionary saving

A welfare analysis of unemployment insurance (UI) is performed in a generalequilibrium job search model. Finitely-lived, risk-averse workers smooth consumption over time by accumulating assets, choose search effort whenunemployed, and suffer disutility from work. Firms hire workers, purchasecapital, and pay taxes to finance worker benefits; their equity is the assetaccumulated by workers. A matching function relates unemployment, hiringexpenditure, and search effort to the formation of jobs. The model is calibrated to US data; the parameters relating job search effort to the probability of job finding are chosen to match microeconomic studies ofunemployment spells. Under logarithmic utility, numerical simulation shows rather small welfaregains from UI. Even without UI, workers smooth consumption effectivelythrough asset accumulation. Greater risk aversion leads to substantiallylarger welfare gains from UI; however, even in this case much of its welfareimpact is due not to consumption smoothing effects, but rather to decreased work disutility, or to a variety of externalities.

Stand Out In A Crowd! Merchandising Your Job Talents,

You want a job. And you believe that somewhere, some employer has precisely the job you want - one that fully utilizes your knowledge and abilities and provides challenge and opportunities for advancement. To find that job, you need to perform a well-planned job search. You have a product to sell - your knowledge, skills and experience . . . YOURSELF! What you need to know is how to market yourself most effectively. Whether you are just out of school and ready to start your career or looking for a new position after 20 years of experience, some of the techniques presented in this booklet may help you. NOTE: ENGLISH

Towards Direct Policy Search Reinforcement Learning for Robot Control

This paper proposes a high-level reinforcement learning (RL) control system for solving the action selection problem of an autonomous robot. Although the dominant approach, when using RL, has been to apply value function based algorithms, the system here detailed is characterized by the use of direct policy search methods. Rather than approximating a value function, these methodologies approximate a policy using an independent function approximator with its own parameters, trying to maximize the future expected reward. The policy based algorithm presented in this paper is used for learning the internal state/action mapping of a behavior. In this preliminary work, we demonstrate its feasibility with simulated experiments using the underwater robot GARBI in a target reaching task

A search-theoretic explanation for the negative correlation between labor income and impatience

Lawrance (1991) has shown, through the estimation of consumption Euler equations, that subjective rates of impatience (time preference) in the U.S. are three to Öve percentage points higher for households with lower average labor incomes than for those with higher labor income. From a theoretical perspective, the sign of this correlation in a job-search model seems at Örst to be undetermined, since more impatient workers tend to accept wage o§ers that less impatient workers would not, thereby remaining less time unemployed. The main result of this paper is showing that, regardless of the existence of e§ects of opposite sign, and independently of the particular speciÖcations of the givens of the model, less impatient workers always end up, in the long run, with a higher average income. The result is based on the (unique) invariant Markov distribution of wages associated with the dynamic optimization problem solved by the consumers. An example is provided to illustrate the method.

Business competition dynamics: agent-based modeling simulations of firms in search of economic performance

A intenção deste trabalho é explorar dinâmicas de competição por meio de “simulação baseada em agentes”. Apoiando-se em um crescente número de estudos no campo da estratégia e teoria das organizações que utilizam métodos de simulação, desenvolveu-se um modelo computacional para simular situações de competição entre empresas e observar a eficiência relativa dos métodos de busca de melhoria de desempenho teorizados. O estudo também explora possíveis explicações para a persistência de desempenho superior ou inferior das empresas, associados às condições de vantagem ou desvantagem competitiva

Job-seeking strategies in Trinidad and Tobago

Includes bibliography

Metaheuristics for Search Problems in Genomics - New Algorithms and Applications

In this thesis we made the first steps towards the systematic application of a methodology for automatically building formal models of complex biological systems. Such a methodology could be useful also to design artificial systems possessing desirable properties such as robustness and evolvability. The approach we follow in this thesis is to manipulate formal models by means of adaptive search methods called metaheuristics. In the first part of the thesis we develop state-of-the-art hybrid metaheuristic algorithms to tackle two important problems in genomics, namely, the Haplotype Inference by parsimony and the Founder Sequence Reconstruction Problem. We compare our algorithms with other effective techniques in the literature, we show strength and limitations of our approaches to various problem formulations and, finally, we propose further enhancements that could possibly improve the performance of our algorithms and widen their applicability. In the second part, we concentrate on Boolean network (BN) models of gene regulatory networks (GRNs). We detail our automatic design methodology and apply it to four use cases which correspond to different design criteria and address some limitations of GRN modeling by BNs. Finally, we tackle the Density Classification Problem with the aim of showing the learning capabilities of BNs. Experimental evaluation of this methodology shows its efficacy in producing network that meet our design criteria. Our results, coherently to what has been found in other works, also suggest that networks manipulated by a search process exhibit a mixture of characteristics typical of different dynamical regimes.