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On the Future of Problem Solving Environments

, 2000
"... In this paper we review the current state of the problem solving environment (PSE) field and make projections for the future. First we describe the computing context, the definition of a PSE and the goals of a PSE. The stateoftheart is summarized along with sources (books, bibliographics, web sit ..."
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Cited by 16 (2 self)
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In this paper we review the current state of the problem solving environment (PSE) field and make projections for the future. First we describe the computing context, the definition of a PSE and the goals of a PSE. The stateoftheart is summarized along with sources (books, bibliographics, web sites) of more detailed information. The principal components and paradigms for building PSEs are presented. The discussion of the future is given in three parts: future trends, scenarios for 2010/2025, and research
SymbolicAlgebraic Computations in a Modeling Language for Mathematical Programming
 In Symbolic Algebraic Methods and Verification
, 2001
"... ..."
Conveying Problem Structure from an Algebraic Modeling Language to Optimization Algorithms
"... : Optimization algorithms can exploit problem structures of various kinds, such as sparsity of derivatives, complementarity conditions, block structure, stochasticity, priorities for discrete variables, and information about piecewiselinear terms. Moreover, some algorithms deduce additional structur ..."
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Cited by 2 (0 self)
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: Optimization algorithms can exploit problem structures of various kinds, such as sparsity of derivatives, complementarity conditions, block structure, stochasticity, priorities for discrete variables, and information about piecewiselinear terms. Moreover, some algorithms deduce additional structural information that may help the modeler. We review and discuss some ways of conveying structure, with examples from our designs for the AMPL modeling language. We show in particular how "declared suffixes" provide a new and useful way to express structure and acquire solution information. 1. INTRODUCTION A modeling language can provide a useful way to express the elaborate optimization problems that often arise in practice. Many of these problems have structure that an optimization algorithm can exploit, such as sparsity of first and second derivatives, complementarity conditions, block structure, timedependent stochasticity, priorities for discrete variables, and information about piecew...
Competition, Transport Infrastructure Investments and CostBenefit Analysis
"... The welfare effects of transport cost reductions resulting from infrastructure improvements are investigated for an asymmetriccosts Cournot oligopoly embedded in a transport network. Transport user’s (direct) benefits are compared to economywide effects in order to assess the socalled indirect ef ..."
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The welfare effects of transport cost reductions resulting from infrastructure improvements are investigated for an asymmetriccosts Cournot oligopoly embedded in a transport network. Transport user’s (direct) benefits are compared to economywide effects in order to assess the socalled indirect effects, not captured in a standard costbenefit analysis. Implications for the first and secondbest rules of investment in infrastructure are derived and their relation with competitionenhancing (weakening) properties of transport capacity expansions is shown to hinge on demand’s concavity (i.e. the fraction of transport cost reductions that is passed on to consumers). Moreover, the magnitude and sign of the ratio of indirect effects to direct benefits depends inversely on the degree of diseconomies of scale and congestion externalities. This ratio has a nonmonotonic relation with the curvature of demand and is negative for transport links with an initial level of demand below a certain threshold. Relying on numerical simulations, within a model calibrated for representative homogeneousgood industries (i.e. cement and steel), the analysis of nonmarginal transport cost reductions ends the paper.
Chapter #999 Conveying Problem Structure from an Algebraic Modeling Language to Optimization Algorithms
"... Optimization, mathematical programming, linear programming, modeling languages Optimization algorithms can exploit problem structures of various kinds, such as sparsity of derivatives, complementarity conditions, block structure, stochasticity, priorities for discrete variables, and information abou ..."
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Optimization, mathematical programming, linear programming, modeling languages Optimization algorithms can exploit problem structures of various kinds, such as sparsity of derivatives, complementarity conditions, block structure, stochasticity, priorities for discrete variables, and information about piecewiselinear terms. Moreover, some algorithms deduce additional structural information that may help the modeler. We review and discuss some ways of conveying structure, with examples from our designs for the AMPL modeling language. We show in particular how Òdeclared suffixesÓ provide a new and useful way to express structure and acquire solution information. 1.
Numerical Issues and Influences in the Design of Algebraic Modeling Languages for Optimization
"... The idea of a modeling language is to describe mathematical problems symbolically in a way that is familiar to people but that allows for processing by computer systems. In particular the concept of an algebraic modeling language, based on objective and constraint expressions in terms of decision va ..."
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The idea of a modeling language is to describe mathematical problems symbolically in a way that is familiar to people but that allows for processing by computer systems. In particular the concept of an algebraic modeling language, based on objective and constraint expressions in terms of decision variables, has proved to be valuable for a broad range of optimization and related problems. One modeling language can work with numerous solvers, each of which implements one or more optimization algorithms. The separation of model specification from solver execution is thus a key tenet of modeling language design. Nevertheless, several issues in numerical analysis that are critical to solvers are also important in implementations of modeling languages. Socalled presolve procedures, which tighten bounds with the aim of eliminating some variables and constraints, are numerical algorithms that require carefully chosen tolerances and can benefit from directed roundings. Correctly rounded binarydecimal conversion is valuable in portably conveying problem instances and in debugging. Further rounding options offer tradeoffs between accuracy, convenience, and readability in displaying
Analysis and Application of Optimization Techniques to Power System Security and Electricity Markets
"... thesis, including any required final revisions, as accepted by my examiners. I understand that my thesis may be made electronically available to the public. Determining the maximum power system loadability, as well as preventing the system from being operated close to the stability limits is very im ..."
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thesis, including any required final revisions, as accepted by my examiners. I understand that my thesis may be made electronically available to the public. Determining the maximum power system loadability, as well as preventing the system from being operated close to the stability limits is very important in power systems planning and operation. The application of optimization techniques to power systems security and electricity markets is a rather relevant research area in power engineering. The study of optimization models to determine critical operating conditions of a power system to obtain secure power dispatches in an electricity market has gained particular attention. This thesis studies and develops optimization models and techniques to detect or avoid voltage instability points in a power system in the context of a competitive electricity market. A thorough analysis of an optimization model to determine the maximum power loadability points is first presented, demonstrating that a solution of this model corresponds to either Saddlenode Bifurcation (SNB) or Limitinduced Bifurcation
IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS–I: FUNDAMENTAL THEORY AND APPLICATIONS 1 Equivalency of Continuation and Optimization Methods to Determine Saddlenode and Limitinduced Bifurcations in Power Systems I: Transversality Conditions
"... Abstract — This paper is the first part of a series of two papers which present a comprehensive and detailed study of an optimizationbased approach to identify and analyze saddlenode bifurcations (SNB) and limitinduced bifurcations (LIB) of a power system model, which are known to be directly asso ..."
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Abstract — This paper is the first part of a series of two papers which present a comprehensive and detailed study of an optimizationbased approach to identify and analyze saddlenode bifurcations (SNB) and limitinduced bifurcations (LIB) of a power system model, which are known to be directly associated with voltage stability problems in these systems. Theoretical studies are presented, formally demonstrating that solution points obtained from an optimization model, which is based on complementarity constraints used to properly represent generators’ voltage controls, correspond to either SNB or LIB points of this model; this is accomplished by showing that optimality conditions of these solution points yield the transversality conditions of the corresponding bifurcation points. A simple but realistic test system is used to numerically illustrate the theoretical discussions. Index Terms — Saddlenode bifurcations, limitinduced bifurcations, transversality conditions, optimization methods, voltage stability, maximum loadability. I.
Conveying Problem Structure to Optimization Algorithms
"... Practical optimization problems can be nontrivial to state, and a modeling language can provide a useful way to express them. Various kinds of structure are needed in optimization algorithms, such as derivatives, complementarity conditions, block structure, stochasticity, priorities for discrete var ..."
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Practical optimization problems can be nontrivial to state, and a modeling language can provide a useful way to express them. Various kinds of structure are needed in optimization algorithms, such as derivatives, complementarity conditions, block structure, stochasticity, priorities for discrete variables, and information about piecewiselinear terms. We review some ways of conveying structure and discuss experience with the AMPL modeling language. In particular, declared suffixes provide a new and useful way to express structure and acquire solution information. 1. Introduction A modeling language can provide a useful way to express the more elaborate optimization problems that often arise in practice. Many of these problems have structure that an optimization algorithm can exploit, such as linear and nonlinear constraints, sparse first and second derivatives, complementarity conditions, block structure, and timedependent stochasticity. Moreover, some algorithms deduce additional s...