Linear programmingLinear programming (LP), also called linear optimization, is a method to achieve the best outcome (such as maximum profit or lowest cost) in a mathematical model whose requirements are represented by linear relationships. Linear programming is a special case of mathematical programming (also known as mathematical optimization). More formally, linear programming is a technique for the optimization of a linear objective function, subject to linear equality and linear inequality constraints.
Integer programmingAn integer programming problem is a mathematical optimization or feasibility program in which some or all of the variables are restricted to be integers. In many settings the term refers to integer linear programming (ILP), in which the objective function and the constraints (other than the integer constraints) are linear. Integer programming is NP-complete. In particular, the special case of 0-1 integer linear programming, in which unknowns are binary, and only the restrictions must be satisfied, is one of Karp's 21 NP-complete problems.
Linear programming relaxationIn mathematics, the relaxation of a (mixed) integer linear program is the problem that arises by removing the integrality constraint of each variable. For example, in a 0–1 integer program, all constraints are of the form The relaxation of the original integer program instead uses a collection of linear constraints The resulting relaxation is a linear program, hence the name.
Feasible regionIn mathematical optimization, a feasible region, feasible set, search space, or solution space is the set of all possible points (sets of values of the choice variables) of an optimization problem that satisfy the problem's constraints, potentially including inequalities, equalities, and integer constraints. This is the initial set of candidate solutions to the problem, before the set of candidates has been narrowed down.
Nonlinear programmingIn mathematics, nonlinear programming (NLP) is the process of solving an optimization problem where some of the constraints or the objective function are nonlinear. An optimization problem is one of calculation of the extrema (maxima, minima or stationary points) of an objective function over a set of unknown real variables and conditional to the satisfaction of a system of equalities and inequalities, collectively termed constraints. It is the sub-field of mathematical optimization that deals with problems that are not linear.
Electric power transmissionElectric power transmission is the bulk movement of electrical energy from a generating site, such as a power plant, to an electrical substation. The interconnected lines that facilitate this movement form a transmission network. This is distinct from the local wiring between high-voltage substations and customers, which is typically referred to as electric power distribution. The combined transmission and distribution network is part of electricity delivery, known as the electrical grid.
Iterative methodIn computational mathematics, an iterative method is a mathematical procedure that uses an initial value to generate a sequence of improving approximate solutions for a class of problems, in which the n-th approximation is derived from the previous ones. A specific implementation with termination criteria for a given iterative method like gradient descent, hill climbing, Newton's method, or quasi-Newton methods like BFGS, is an algorithm of the iterative method.
Assignment problemThe assignment problem is a fundamental combinatorial optimization problem. In its most general form, the problem is as follows: The problem instance has a number of agents and a number of tasks. Any agent can be assigned to perform any task, incurring some cost that may vary depending on the agent-task assignment. It is required to perform as many tasks as possible by assigning at most one agent to each task and at most one task to each agent, in such a way that the total cost of the assignment is minimized.
European super gridThe European super grid is a possible future super grid that would ultimately interconnect the various European countries and the regions around Europe's borders – including North Africa, Kazakhstan, and Turkey – with a high-voltage direct current (HVDC) power grid.
Market (economics)In economics, a market is a composition of systems, institutions, procedures, social relations or infrastructures whereby parties engage in exchange. While parties may exchange goods and services by barter, most markets rely on sellers offering their goods or services (including labour power) to buyers in exchange for money. It can be said that a market is the process by which the prices of goods and services are established. Markets facilitate trade and enable the distribution and allocation of resources in a society.
Electrical gridAn electrical grid is an interconnected network for electricity delivery from producers to consumers. Electrical grids vary in size and can cover whole countries or continents. It consists of: power stations: often located near energy and away from heavily populated areas electrical substations to step voltage up or down electric power transmission to carry power long distances electric power distribution to individual customers, where voltage is stepped down again to the required service voltage(s).
Wide area synchronous gridA wide area synchronous grid (also called an "interconnection" in North America) is a three-phase electric power grid that has regional scale or greater that operates at a synchronized utility frequency and is electrically tied together during normal system conditions. Also known as synchronous zones, the most powerful is the Northern Chinese State Grid with 1,700 gigawatts (GW) of generation capacity, while the widest region served is that of the IPS/UPS system serving most countries of the former Soviet Union.
Euler methodIn mathematics and computational science, the Euler method (also called the forward Euler method) is a first-order numerical procedure for solving ordinary differential equations (ODEs) with a given initial value. It is the most basic explicit method for numerical integration of ordinary differential equations and is the simplest Runge–Kutta method. The Euler method is named after Leonhard Euler, who first proposed it in his book Institutionum calculi integralis (published 1768–1870).
Smart gridA smart grid is an electrical grid which includes a variety of operation and energy measures including: Advanced metering infrastructure (of which smart meters are a generic name for any utility side device even if it is more capable e.g. a fiber optic router) Smart distribution boards and circuit breakers integrated with home control and demand response (behind the meter from a utility perspective) Load control switches and smart appliances, often financed by efficiency gains on municipal programs (e.g.
Real-time computingReal-time computing (RTC) is the computer science term for hardware and software systems subject to a "real-time constraint", for example from event to system response. Real-time programs must guarantee response within specified time constraints, often referred to as "deadlines". Real-time responses are often understood to be in the order of milliseconds, and sometimes microseconds. A system not specified as operating in real time cannot usually guarantee a response within any timeframe, although typical or expected response times may be given.
Electricity marketIn a broad sense, an electricity market is a system that facilitates the exchange of electricity-related goods and services. During more than a century of evolution of the electric power industry, the economics of the electricity markets had undergone enormous changes for reasons ranging from the technological advances on supply and demand sides to politics and ideology.
Cutting-plane methodIn mathematical optimization, the cutting-plane method is any of a variety of optimization methods that iteratively refine a feasible set or objective function by means of linear inequalities, termed cuts. Such procedures are commonly used to find integer solutions to mixed integer linear programming (MILP) problems, as well as to solve general, not necessarily differentiable convex optimization problems. The use of cutting planes to solve MILP was introduced by Ralph E. Gomory.
Simplex algorithmIn mathematical optimization, Dantzig's simplex algorithm (or simplex method) is a popular algorithm for linear programming. The name of the algorithm is derived from the concept of a simplex and was suggested by T. S. Motzkin. Simplices are not actually used in the method, but one interpretation of it is that it operates on simplicial cones, and these become proper simplices with an additional constraint. The simplicial cones in question are the corners (i.e., the neighborhoods of the vertices) of a geometric object called a polytope.
LiberalizationLiberalization or liberalisation (British English) is a broad term that refers to the practice of making laws, systems, or opinions less severe, usually in the sense of eliminating certain government regulations or restrictions. The term is used most often in relation to economics, where it refers to economic liberalization, the removal or reduction of restrictions placed upon (a particular sphere of) economic activity.
Free marketIn economics, a free market is an economic system in which the prices of goods and services are determined by supply and demand expressed by sellers and buyers. Such markets, as modeled, operate without the intervention of government or any other external authority. Proponents of the free market as a normative ideal contrast it with a regulated market, in which a government intervenes in supply and demand by means of various methods such as taxes or regulations.
