다중혈관 관상동맥 환자에서 y-문합을 이용하여 양쪽 내흉동맥만을 사용한 우회술의 조기 성적

Mitigation from a cross-sectoral perspective

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The Theory of Industrial Organization

This chapter discusses leading problems linked to energy that the world is now confronting and to propose some ideas concerning possible solutions. Oil deserves special attention among all energy sources. Since the beginning of 1981, it has merely been continuing and enhancing the downward movement in consumption and prices caused by excessive rises, especially for light crudes such as those from Africa, and the slowing down of worldwide economic growth. Densely-populated oil-producing countries need to produce to live, to pay for their food and their equipment. If the economic growth of the industrialized countries were to be 4%, even if investment in the rational use of energy were pushed to the limit and the development of nonpetroleum energy sources were also pursued actively, it would be extremely difficult to prevent a sharp rise in prices. It is evident that it is absolutely necessary to pursue actively the development of coal, natural gas, and nuclear power if a physical shortage of energy is not to block economic growth.

World energy outlook

Introduction to stochastic programming

This addition to the ISOR series introduces complementarity models in a straightforward and approachable manner and uses them to carry out an in-depth analysis of energy markets, including formulation issues and solution techniques. In a nutshell, complementarity models generalize: a. optimization problems via their Karush-Kuhn-Tucker conditions b. on-cooperative games in which each player may be solving a separate but related optimization problem with potentially overall system constraints (e.g., market-clearing conditions) c. conomic and engineering problems that arent specifically derived from optimization problems (e.g., spatial price equilibria) d. roblems in which both primal and dual variables (prices) appear in the original formulation (e.g., The National Energy Modeling System (NEMS) or its precursor, PIES). As such, complementarity models are a very general and flexible modeling format. A natural question is why concentrate on energy markets for this complementarity approach? s it turns out, energy or other markets that have game theoretic aspects are best modeled by complementarity problems. The reason is that the traditional perfect competition approach no longer applies due to deregulation and restructuring of these markets and thus the corresponding optimization problems may no longer hold. Also, in some instances it is important in the original model formulation to involve both primal variables (e.g., production) as well as dual variables (e.g., market prices) for public and private sector energy planning. Traditional optimization problems can not directly handle this mixing of primal and dual variables but complementarity models can and this makes them all that more effective for decision-makers.

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Complementarity Modeling in Energy Markets

In this paper, we present a new iterative method for solving the nonlinear complementarity problem. This method, which we call NE/SQP (for Nonsmooth Equations/Successive Quadratic Programming), is a damped Gauss--Newton algorithm applied to solve a certain nonsmooth-equation formulation of the complementarity problem; it is intended to overcome a major deficiency of several previous methods of this type. Unlike these earlier algorithms whose convergence critically depends on a solvability assumption on the subproblems, the NE/SQP method involves solving a sequence of nonnegatively constrained convex quadratic programs of the least-squares type; the latter programs are always solvable and their solution can be obtained by a host of efficient quadratic programming subroutines. Hence, the new method is a robust procedure which, not only is very easy to describe and simple to implement, but also has the potential advantage of being capable of solving problems of very large size. Besides the desirable feature of robustness and ease of implementation, the NE/SQP method retains two fundamental attractions of a typical member in the Gauss--Newton family of algorithms; namely, it is globally and locally quadratically convergent. Besides presenting the detailed description of the NE/SQP method and the associated convergence theory, we also report the numerical results of an extensive computational study which is aimed at demonstrating the practical efficiency of the method for solving a wide variety of realistic nonlinear complementarity problems.

NE/SQP: A robust algorithm for the nonlinear complementarity problem

https://www.diw.de/documents/publikationen/73/diw_01.c.69083.de/dp732.pdf

A Complementarity Model for the European Natural Gas Market

In this paper we present a version of the (static) traffic equilibrium problem in which the cost incurred on each path is not simply the sum of the costs on the arcs that constitute that path We motivate this nonadditive version of the problem by describing several situations in which the classic additivity assumption fails We describe existence and uniqueness conditions for this problem, and we also present convergence theory for ageneric algorithm for solving nonadditive problems

/pdf/the-traffic-equilibrium-problem-with-nonadditive-path-costs-1pcfxk8izq.pdf

Steven A. Gabriel

Papers

Complementarity Modeling in Energy Markets

NE/SQP: A robust algorithm for the nonlinear complementarity problem

A Complementarity Model for the European Natural Gas Market

The Traffic Equilibrium Problem with Nonadditive Path Costs

Solving discretely-constrained MPEC problems with applications in electric power markets