Thomas L. Magnanti and Georgia Perakis
... are shared by all these algorithms: they all generate a sequence of "nice" sets of the same type, and use the notion of a center of a "nice" set. At each iteration, the general framework maintains a convex set that is known to contain all solutions of the variational inequality problem and "cuts" th ...
... are shared by all these algorithms: they all generate a sequence of "nice" sets of the same type, and use the notion of a center of a "nice" set. At each iteration, the general framework maintains a convex set that is known to contain all solutions of the variational inequality problem and "cuts" th ...
Introduction to Geometry
... 60 = 70 , so the angles of 4ABC match those of 4DFE. In the same way, if we ever have two angles of one triangle equal to two angles of another, we know that the third angles in the two triangles are equal. Measuring, we find that the ratios are each about 2/3. It appears to be the case that if all ...
... 60 = 70 , so the angles of 4ABC match those of 4DFE. In the same way, if we ever have two angles of one triangle equal to two angles of another, we know that the third angles in the two triangles are equal. Measuring, we find that the ratios are each about 2/3. It appears to be the case that if all ...
Learning to Solve Complex Planning Problems
... interrupt may not give the planner the opportunity to explore a rich enough search space. On the other hand, an excessively long partial search episode, aside from taking a long time, may mislead our learning algorithm in its attempt to extract the relevant information. It may even be the case that ...
... interrupt may not give the planner the opportunity to explore a rich enough search space. On the other hand, an excessively long partial search episode, aside from taking a long time, may mislead our learning algorithm in its attempt to extract the relevant information. It may even be the case that ...
Lower Bounds for the Relative Greedy Algorithm for Approximating
... The second lower bound is obtained by constructing an instance G k,l which places the instance Gk into a grid. The instance Gk,l consists of an 4k × l grid of terminals where the last terminals of each column have been identified as one terminal. For each column of terminals the graph Gk − Tb − Tc i ...
... The second lower bound is obtained by constructing an instance G k,l which places the instance Gk into a grid. The instance Gk,l consists of an 4k × l grid of terminals where the last terminals of each column have been identified as one terminal. For each column of terminals the graph Gk − Tb − Tc i ...
An Algorithm for Solving Scaled Total Least Squares Problems
... we know, computing the SVD is expensive. In this paper, we present an algorithm for solving the STLS problem using a rank revealing decomposition. This algorithm is more efficient than the SVD method and it is particularly efficient for the STLS problems with same coefficient matrix A but multiple r ...
... we know, computing the SVD is expensive. In this paper, we present an algorithm for solving the STLS problem using a rank revealing decomposition. This algorithm is more efficient than the SVD method and it is particularly efficient for the STLS problems with same coefficient matrix A but multiple r ...
4.2 Law of Cosines - Art of Problem Solving
... 60 east of north at 32 km/h. If the plane has enough fuel for 5 hours of flying, what is the maximum distance south the pilot can travel, so that the fuel remaining will allow a safe return to the carrier? (You may assume Earth is flat in this problem.) (Source: CEMC) Solution for Problem 4.10: We s ...
... 60 east of north at 32 km/h. If the plane has enough fuel for 5 hours of flying, what is the maximum distance south the pilot can travel, so that the fuel remaining will allow a safe return to the carrier? (You may assume Earth is flat in this problem.) (Source: CEMC) Solution for Problem 4.10: We s ...
Knapsack problem
The knapsack problem or rucksack problem is a problem in combinatorial optimization: Given a set of items, each with a mass and a value, determine the number of each item to include in a collection so that the total weight is less than or equal to a given limit and the total value is as large as possible. It derives its name from the problem faced by someone who is constrained by a fixed-size knapsack and must fill it with the most valuable items.The problem often arises in resource allocation where there are financial constraints and is studied in fields such as combinatorics, computer science, complexity theory, cryptography and applied mathematics.The knapsack problem has been studied for more than a century, with early works dating as far back as 1897. It is not known how the name ""knapsack problem"" originated, though the problem was referred to as such in the early works of mathematician Tobias Dantzig (1884–1956), suggesting that the name could have existed in folklore before a mathematical problem had been fully defined.