Geometric programming: Duality in quadratic programming and lp-approximation III (degenerate programs)
نویسندگان
چکیده
منابع مشابه
Geometric Duality and Linear Programming
Linear programs are problems that involve the optimization of a linear objective function subject to linear constraints. Every linear program has an inherent geometric representation. Each constraint defines an halfspace and the feasible region of the the linear program is the convex polyhedron defined by intersection of all the halfspaces. The maximal solution to the linear program (if it exis...
متن کاملSensitivity analysis in (degenerate) quadratic programming
In this paper we deal with sensitivity analysis in convex quadratic programming, without making assumptions on nondegeneracy, strict convexity of the objective function, and the existence of a strictly complementary solution. We show that the optimal value as a function of a right{hand side element (or an element of the linear part of the objective) is piecewise quadratic, where the pieces can ...
متن کاملOn duality gap in binary quadratic programming
We present in this paper new results on the duality gap between the binary quadratic optimization problem and its Lagrangian dual or semidefinite programming relaxation. We first derive a necessary and sufficient condition for the zero duality gap and discuss its relationship with the polynomial solvability of the primal problem. We then characterize the zeroness of the duality gap by the dista...
متن کاملApproximation Algorithms for Quadratic Programming
We consider the problem of approximating the global minimum of a general quadratic program (QP) with n variables subject to m ellipsoidal constraints. For m = 1, we rigorously show that an-minimizer, where error 2 (0; 1), can be obtained in polynomial time, meaning that the number of arithmetic operations is a polynomial in n, m, and log(1==). For m 2, we present a polynomial-time (1 ? 1 m 2)-a...
متن کاملGeometric Duality in Multiple Objective Linear Programming
We develop in this article a geometric approach to duality in Multiple Objective Linear Programming. This approach is based on a very old idea, the duality of polytopes, which can be traced back to the old Greeks. We show that there is an inclusion reversing one-to-one map between the minimal faces of the image of the primal objective and the maximal faces of the image of the dual objective map.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Mathematical Analysis and Applications
سال: 1970
ISSN: 0022-247X
DOI: 10.1016/0022-247x(70)90085-5