Strong Duality for Semidefinite Programming
نویسندگان
چکیده
منابع مشابه
Strong Duality for Semidefinite Programming
It is well known that the duality theory for linear programming (LP) is powerful and elegant and lies behind algorithms such as simplex and interior-point methods. However, the standard Lagrangian for nonlinear programs requires constraint qualifications to avoid duality gaps. Semidefinite linear programming (SDP) is a generalization of LP where the nonnegativity constraints are replaced by a s...
متن کاملLocal Duality of Nonlinear Semidefinite Programming
In a recent paper [8], Chan and Sun reported for semidefinite programming (SDP) that the primal/dual constraint nondegeneracy is equivalent to the dual/primal strong second order sufficient condition (SSOSC). This result is responsible for a number of important results in stability analysis of SDP. In this paper, we study duality of this type in nonlinear semidefinite programming (NSDP). We int...
متن کاملOn duality theory for non-convex semidefinite programming
In this paper, with the help of convex-like function, we discuss the duality theory for nonconvex semidefinite programming. Our contributions are: duality theory for the general nonconvex semidefinite programming when Slater’s condition holds; perfect duality for a special case of the nonconvex semidefinite programming for which Slater’s condition fails. We point out that the results of [2] can...
متن کاملSensitivity analysis of semidefinite programs without strong duality
Suppose that we are given a feasible conic program with a finite optimal value and with strong duality failing. It is known that there are small perturbations of the problem data that lead to relatively big changes in the optimal value. We quantify the notion of big change in the case of a semidefinite program (SDP). We first show that for any SDP with a finite optimal value where strong dualit...
متن کاملWEAK AND STRONG DUALITY THEOREMS FOR FUZZY CONIC OPTIMIZATION PROBLEMS
The objective of this paper is to deal with the fuzzy conic program- ming problems. The aim here is to derive weak and strong duality theorems for a general fuzzy conic programming. Toward this end, The convexity-like concept of fuzzy mappings is introduced and then a speci c ordering cone is established based on the parameterized representation of fuzzy numbers. Un- der this setting, duality t...
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: SIAM Journal on Optimization
سال: 1997
ISSN: 1052-6234,1095-7189
DOI: 10.1137/s1052623495288350