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.
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.
Sorting algorithmIn computer science, a sorting algorithm is an algorithm that puts elements of a list into an order. The most frequently used orders are numerical order and lexicographical order, and either ascending or descending. Efficient sorting is important for optimizing the efficiency of other algorithms (such as search and merge algorithms) that require input data to be in sorted lists. Sorting is also often useful for canonicalizing data and for producing human-readable output.
Urban planningUrban planning, also known as town planning, city planning, regional planning, or rural planning, is a technical and political process that is focused on the development and design of land use and the built environment, including air, water, and the infrastructure passing into and out of urban areas, such as transportation, communications, and distribution networks and their accessibility.
Unimodular matrixIn mathematics, a unimodular matrix M is a square integer matrix having determinant +1 or −1. Equivalently, it is an integer matrix that is invertible over the integers: there is an integer matrix N that is its inverse (these are equivalent under Cramer's rule). Thus every equation Mx = b, where M and b both have integer components and M is unimodular, has an integer solution. The n × n unimodular matrices form a group called the n × n general linear group over , which is denoted .
Apollo programThe Apollo program, also known as Project Apollo, was the third United States human spaceflight program carried out by the National Aeronautics and Space Administration (NASA), which succeeded in preparing and landing the first humans on the Moon from 1968 to 1972. It was first conceived in 1960 during President Dwight D. Eisenhower's administration as a three-person spacecraft to follow the one-person Project Mercury, which put the first Americans in space. Apollo was later dedicated to President John F.
Instrument landing systemIn aviation, the instrument landing system (ILS) is a precision radio navigation system that provides short-range guidance to aircraft to allow them to approach a runway at night or in bad weather. In its original form, it allows an aircraft to approach until it is over the ground, within a of the runway. At that point the runway should be visible to the pilot; if it is not, they perform a missed approach. Bringing the aircraft this close to the runway dramatically increases the range of weather conditions in which a safe landing can be made.
Shor's algorithmShor's algorithm is a quantum algorithm for finding the prime factors of an integer. It was developed in 1994 by the American mathematician Peter Shor. It is one of the few known quantum algorithms with compelling potential applications and strong evidence of superpolynomial speedup compared to best known classical (that is, non-quantum) algorithms. On the other hand, factoring numbers of practical significance requires far more qubits than available in the near future.
Divide-and-conquer algorithmIn computer science, divide and conquer is an algorithm design paradigm. A divide-and-conquer algorithm recursively breaks down a problem into two or more sub-problems of the same or related type, until these become simple enough to be solved directly. The solutions to the sub-problems are then combined to give a solution to the original problem. The divide-and-conquer technique is the basis of efficient algorithms for many problems, such as sorting (e.g., quicksort, merge sort), multiplying large numbers (e.
Utility cyclingUtility cycling encompasses any cycling done simply as a means of transport rather than as a sport or leisure activity. It is the original and most common type of cycling in the world. Cycling mobility is one of the various types of private transport and a major part of individual mobility. Utility or "transportational" cycling generally involves traveling short and medium distances (several kilometres, not uncommonly 3–15 kilometres one way, or somewhat longer), often in an urban environment. It includes commuting (i.
