### Table 2: Duality for closed conic convex programs

"... In PAGE 23: ...d #03 = inf 8 #3E #3C #3E : s 5 #0C #0C #0C #0C #0C #0C #0C 2 6 4 0 1 0 1 s 2 s 5 = p 2 0 s 5 = p 2 0 3 7 5 #17 0 9 #3E = #3E ; = 1: Finally, the possibility of the entries in Table2 where weak infeasibility is not involved, can be demonstrated by a 2-dimensional linear programming problem: Example 5 Let n =2,c2#3C 2 ,K=K #03 =#3C 2 + and A = f#28x 1 ;x 2 #29jx 1 =0g; A ? =f#28s 1 ;s 2 #29js 2 =0g: We see that #28P#29 is strongly feasible if c 1 #3E 0,weakly feasible if c 1 =0and strongly infeasible if c 1 #3C 0. Similarly, #28D#29 is strongly feasible if c 2 #3E 0,weakly feasible if c 2 =0and strongly infeasible if c 2 #3C 0.... In PAGE 27: ... #0F The regularizedprogram CP#28b; c; A; K 0 #29 is dual strongly infeasible if and only if F D = ;. Combining Theorem 8 with Table2 , we see that the regularized conic convex program is in perfect duality: Corollary 7 Assume the same setting as in Theorem 8. Then there holds #0F If d #03 = 1, then the regularized primal CP#28b; c; A; K 0 #29 is either infeasible or unbounded.... ..."

### Table I. Basic terms and notation for linear (LP), semidefinite (SDP), and conic programming. Term LP SDP Conic Notation

2005

Cited by 11

### Table 3: Bounds from Semidefinite Programming. (Intel Pentium III, 933 MHz). 30

2004

### Table 3: Bounds from Semidefinite Programming. (Intel Pentium III, 933 MHz). 30

2004

### Table 4: Cost of network design, duality gap and comparison

1995

"... In PAGE 15: ... Finally, if we compare the primal cost for the multi- hour design with the dual cost for the single-hour design we, in essence, get a feel for the \worst quot; case saving achieved by MuH approach since the (actual) optimal dual objective for MaxBH case provides us with the maximum possible value that the primal cost could possibly go down to if static VP routing were used. The cost results for the example networks with multi-hour tra c and maximum busy hour tra c are tabulated in Table4 using the decomposition algorithm of the previous section. In this table, we show the best cost for problem (P), the best cost for Mixed integer program (MIP), the best dual cost, the LSPH cost as well as the duality gap and saving of dual-based decomposition algorithm compared to LSPH.... In PAGE 15: ... Furthermore, observe that our decomposition algorithm method provides between 6 % and 20 % cost saving compared to the local shortest path heuristic. In Table 5, we show the iteration number when the lowest primal value, CP , reported in Table4 is obtained along with the computing time in seconds (step 2 and step 3) for running to 1000 dual iterations; this is on a DEC Alpha AXP running OSF/1 operating system (DEC Model 3000/400, 64MB main memory, SPECfp 92 benchmark = 112.5).... ..."

Cited by 18

### Table 1: Algorithm: Semidefinite Embedding (SDE).

2005

Cited by 2

### Table 1: Duality

2006

"... In PAGE 21: ...roof. See Jockusch/Shore [12, Theorem 3.1]. We shall see that the Duality Theorem provides a powerful method of passing from lowness properties to highness properties as in Table1 . The meaning of Table 1 is that, if we have a uniformly relativizable construction of an r.... In PAGE 21: ...roof. See Jockusch/Shore [12, Theorem 3.1]. We shall see that the Duality Theorem provides a powerful method of passing from lowness properties to highness properties as in Table 1. The meaning of Table1 is that, if we have a uniformly relativizable construction of an r.e.... ..."

Cited by 5

### Table 1: Duality

"... In PAGE 21: ...roof. See Jockusch/Shore [12, Theorem 3.1]. square We shall see that the Duality Theorem provides a powerful method of passing from lowness properties to highness properties as in Table1 . The meaning of Table 1 is that, if we have a uniformly relativizable construction of an r.... In PAGE 21: ...roof. See Jockusch/Shore [12, Theorem 3.1]. square We shall see that the Duality Theorem provides a powerful method of passing from lowness properties to highness properties as in Table 1. The meaning of Table1 is that, if we have a uniformly relativizable construction of an r.e.... ..."

### Table 1 Galerkin duality vs. electromagnetic duality Galerkin duality Electromagnetic duality

in Abstract

2005