A polynomial algorithm in linear programmingSee the review of the English translation Sov. Math., Dokl. 20, 191‒194 (1979) in Zbl 0409.90079.doi:10.1016/0041-5553(80)90061-0Khachiyan, LeonidDoklady Adademiia Nauk Cccp
Over the rationals, the general linear programming problem is equivalent to the convex hull problem of determining if a given m 脳 n matrix H has a nontrivial nonnegative zero. We give a polynomial time algorithm that either finds a nontrivial nonnegative zero of H , or it obtains a ...
Linear Programming ProblemsIn this paper a method for solving perfect systems of linear inequalities is presented. It is based on selecting and removing inessential constraints. This method is a strongly polynomial one for the class of systems of inequalities with a constant difference between the ...
Khachiyan LG (1979) A polynomial algorithm in linear programming. Sov Math Doklady 20:191–194 MATH Google Scholar Liang GS, Wang MJ (1993) A fuzzy multi-criteria decision-making approach for robot selection. Robot CIM-INT 10(4):267–274 Article Google Scholar Liou T-S, Wang M-JJ (...
Linear programmingPROJECTIONSYSTEMSThis article proposes a polynomial-time algorithm for convex quadratic optimization subject to linear inequalities. The running time of the algorithm is polynomial in the binary size of the input data and in the logarithm of the reciprocal of the given accuracy....
Linear programming was first introduced by Leonid Kantorovich in 1939 and then independently reintroduced by George Dantzig in 1947. Dantzig developed the first algorithm for solving linear programming problems, called the “simplex” method. Remarkably, this decades-old algorithm remains one of the mos...
Dantzig developed the first algorithm for solving linear programming problems, called the “simplex” method. Remarkably, this decades-old algorithm remains one of the most efficient and reliable methods for solving such problems today. Learn more about the simplex method in practice. How Does the ...
To improve the efficiency further, we develop another algorithm, MIN-T-DEPTH, whose complexity depends on some conjectures that have been motivated by the polynomial complexity algorithm in ref. 23 for synthesizing T-count optimal circuits. At this point, our conjectures do not seem to be derived...
[7] introduce a new feasible corrector-predictor interior-point algorithm for P∗(κ)-LCP by using the method of algebraically equivalent transform of the nonlinear equation of the system and obtain the polynomial complexity O((1+2κ)nlog9nμo8ϵ). This complexity is still the best ...
However, this FPTAS relies on two very restrictive conditions: (i) the problem tackled must present a pseudopolynomial algorithm, and (ii) the corresponding classical counterpart has to be polynomially solvable. Condition (ii) comes from the fact that the aforementioned FPTAS uses AMU within its ...