Optimization in the context of Algorithmic mechanism design


Optimization in the context of Algorithmic mechanism design

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⭐ Core Definition: Optimization

Mathematical optimization (alternatively spelled optimisation) or mathematical programming is the selection of a best element, with regard to some criteria, from some set of available alternatives. It is generally divided into two subfields: discrete optimization and continuous optimization. Optimization problems arise in all quantitative disciplines from computer science and engineering to operations research and economics, and the development of solution methods has been of interest in mathematics for centuries.

In the more general approach, an optimization problem consists of maximizing or minimizing a real function by systematically choosing input values from within an allowed set and computing the value of the function. The generalization of optimization theory and techniques to other formulations constitutes a large area of applied mathematics.

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👉 Optimization in the context of Algorithmic mechanism design

Algorithmic mechanism design (AMD) lies at the intersection of economic game theory, optimization, and computer science. The prototypical problem in mechanism design is to design a system for multiple self-interested participants, such that the participants' self-interested actions at equilibrium lead to good system performance. Typical objectives studied include revenue maximization and social welfare maximization. Algorithmic mechanism design differs from classical economic mechanism design in several respects. It typically employs the analytic tools of theoretical computer science, such as worst case analysis and approximation ratios, in contrast to classical mechanism design in economics which often makes distributional assumptions about the agents. It also considers computational constraints to be of central importance: mechanisms that cannot be efficiently implemented in polynomial time are not considered to be viable solutions to a mechanism design problem. This often, for example, rules out the classic economic mechanism, the Vickrey–Clarke–Groves auction.

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Optimization in the context of Asset management

Asset management is a systematic approach to the governance and realization of all value for which a group or entity is responsible. It may apply both to tangible assets (physical objects such as complex process or manufacturing plants, infrastructure, buildings or equipment) and to intangible assets (such as intellectual property, goodwill or financial assets). Asset management is a systematic process of developing, operating, maintaining, upgrading, and disposing of assets in the most cost-effective manner (including all costs, risks, and performance attributes).

Theory of asset management primarily deals with the periodic matter of improving, maintaining or in other circumstances assuring the economic and capital value of an asset over time. The term is commonly used in engineering, the business world, and public infrastructure sectors to ensure a coordinated approach to the optimization of costs, risks, service/performance, and sustainability. The term has traditionally been used in the financial sector to describe people and companies who manage investments on behalf of others. Those include, for example, investment managers who manage the assets of a pension fund.

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Optimization in the context of Management science

Management science (or managerial science) is a wide and interdisciplinary study of solving complex problems and making strategic decisions as it pertains to institutions, corporations, governments and other types of organizational entities. It is closely related to management, economics, business, engineering, management consulting, and other fields. It uses various scientific research-based principles, strategies, and analytical methods including mathematical modeling, statistics and numerical algorithms and aims to improve an organization's ability to enact rational and accurate management decisions by arriving at optimal or near optimal solutions to complex decision problems.

Management science looks to help businesses achieve goals using a number of scientific methods. The field was initially an outgrowth of applied mathematics, where early challenges were problems relating to the optimization of systems which could be modeled linearly, i.e., determining the optima (maximum value of profit, assembly line performance, crop yield, bandwidth, etc. or minimum of loss, risk, costs, etc.) of some objective function. Today, the discipline of management science may encompass a diverse range of managerial and organizational activity as it regards to a problem which is structured in mathematical or other quantitative form in order to derive managerially relevant insights and solutions.

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Optimization in the context of Choice modelling

Choice modelling attempts to model the decision process of an individual or segment via revealed preferences or stated preferences made in a particular context or contexts. Typically, it attempts to use discrete choices (A over B; B over A, B & C) in order to infer positions of the items (A, B and C) on some relevant latent scale (typically "utility" in economics and various related fields). Indeed many alternative models exist in econometrics, marketing, sociometrics and other fields, including utility maximization, optimization applied to consumer theory, and a plethora of other identification strategies which may be more or less accurate depending on the data, sample, hypothesis and the particular decision being modelled. In addition, choice modelling is regarded as the most suitable method for estimating consumers' willingness to pay for quality improvements in multiple dimensions.

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Optimization in the context of Non-ferrous extractive metallurgy

Non-ferrous extractive metallurgy is one of the two branches of extractive metallurgy which pertains to the processes of reducing valuable, non-iron metals from ores or raw material. Metals like zinc, copper, lead, aluminium as well as rare and noble metals are of particular interest in this field, while the more common metal, iron, is considered a major impurity. Like ferrous extraction, non-ferrous extraction primarily focuses on the economic optimization of extraction processes in separating qualitatively and quantitatively marketable metals from its impurities (gangue).

Any extraction process will include a sequence of steps or unit processes for separating highly pure metals from undesirables in an economically efficient system. Unit processes are usually broken down into three categories: pyrometallurgy, hydrometallurgy, and electrometallurgy. In pyrometallurgy, the metal ore is first oxidized through roasting or smelting. The target metal is further refined at high temperatures and reduced to its pure form. In hydrometallurgy, the object metal is first dissociated from other materials using a chemical reaction, which is then extracted in pure form using electrolysis or precipitation. Finally, electrometallurgy generally involves electrolytic or electrothermal processing. The metal ore is either distilled in an electrolyte or acid solution, then magnetically deposited onto a cathode plate (electrowinning); or smelted then melted using an electric arc or plasma arc furnace (electrothermic reactor).

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