### Table 1: Optimization program for linear lossy compressions

in Abstract

"... In PAGE 5: ... 5. Table1 outlines a simple optimization program to find lossy compressions that minimize a weighted sum of the max-norm residual errors, a0a2a1 and a0a4a3 , in Eq. 5.... In PAGE 6: ... 4.2 Structured Compressions As with lossless compressions, solving the program in Table1 may be intractable due to the size of a0 . There are a48 a29a7a12a25 a0 a25 a17 constraints and a25 a0 a25a18a25 a35 a0 a25 unknown entries in matrix a5 .... In PAGE 6: ... One approach is related to the basis function model proposed in [4], in which we restrict a5 to be functions over some small set of factors (subsets of state variables.) This ensures that the number of unknown parameters in any column of a5 (which we optimize in Table1 ) is 3Assuming a49 a50 is small, the a51a9a49 a50 a51 a52 variables in each a49 a53a55a54a9a56 a57 and a51a9a49 a50 a51 variables in a49 a106... In PAGE 7: ... These techniques are rather involved, so we refer to the cited papers for details. By searching within a restricted set of structured compressions and by exploiting DBN structure it is possible to efficiently solve the optimization program in Table1 . The question of factor selection remains: on what factors should a5 be defined? A version of this question has been tackled in [12, 14] in the context of selecting a basis to approximately solve MDPs.... In PAGE 7: ...1. For further com- pression, we applied the optimization program described in Table1 by setting the weights a5 and a6 to a37 and a15 a53a30a53a30 respectively. The alternating variable technique was iterated a37 a8a7 a30 times, with the best solution chosen from a37 a8a7 random restarts (to mitigate the effects of local op- tima).... ..."

### Table 1: Optimization program for linear lossy compressions

in Abstract

"... In PAGE 5: ... 5. Table1 outlines a simple optimization program to find lossy compressions that minimize a weighted sum of the max-norm residual errors, a0a2a1 and a0a4a3 , in Eq. 5.... In PAGE 6: ... 4.2 Structured Compressions As with lossless compressions, solving the program in Table1 may be intractable due to the size of a0 . There are a48 a29a7a12a25 a0 a25 a17 constraints and a25 a0 a25a18a25 a35 a0 a25 unknown entries in matrix a5 .... In PAGE 6: ... One approach is related to the basis function model proposed in [4], in which we restrict a5 to be functions over some small set of factors (subsets of state variables.) This ensures that the number of unknown parameters in any column of a5 (which we optimize in Table1 ) is 3Assuming a49 a50 is small, the a51a9a49 a50 a51 a52 variables in each a49 a53a55a54a9a56 a57 and a51a9a49 a50 a51 variables in a49 a104... In PAGE 7: ... These techniques are rather involved, so we refer to the cited papers for details. By searching within a restricted set of structured compressions and by exploiting DBN structure it is possible to efficiently solve the optimization program in Table1 . The question of factor selection remains: on what factors should a5 be defined? A version of this question has been tackled in [12, 14] in the context of selecting a basis to approximately solve MDPs.... In PAGE 7: ...1. For further com- pression, we applied the optimization program described in Table1 by setting the weights a5 and a6 to a37 and a15 a53a30a53a30 respectively. The alternating variable technique was iterated a37 a8a7 a30 times, with the best solution chosen from a37 a8a7 random restarts (to mitigate the effects of local op- tima).... ..."

### TABLE I Linear programming formulation for optimal routing.

2004

Cited by 3

### TABLE I LINEAR PROGRAM FOR DETERMINING OPTIMAL COLLABORATIVE STRATEGY

### TABLE I LINEAR PROGRAM FOR DETERMINING OPTIMAL COLLABORATIVE STRATEGY

### TABLE I LINEAR PROGRAM FOR DETERMINING OPTIMAL COLLABORATIVE STRATEGY

### TABLE I Quadratic placementand#0C-regularization compared against optimal linear programming results. Total wirelength

### Table 1: Summary of the sizes of the optimization problems for different norms. (See Appendix B for the definitions of the constraints in linear programming.)

2000

"... In PAGE 7: ... In contrast, in our framework the confidence C3B4DCBN AM C5DDB5 is com- pared to D1CPDCD6BI BPDD C3B4DCBN AM C5D6B5 and has only D1 slack variables in the primal program. In Table1 we summarize the properties of the program- s discussed above. As shown in the table, the advantage of using D0BE in the objective function is that the number of vari- ables in the dual problem in only a function of on CZ and D1 and does not depend on the number columns D0 in C5.... In PAGE 7: ... (24) can be solved using standard QP techniques. As shown in Table1 the dual program depends on D1CZ variables and has CZD1 B7 D1 con- straints all together. Converting the dual program in Eq.... ..."

Cited by 79

### Table 1: Summary of the sizes of the optimization problems for different norms. (See Appendix B for the definitions of the constraints in linear programming.)

2000

"... In PAGE 7: ... In contrast, in our framework the confidence C3B4DCBN AM C5DDB5 is com- pared to D1CPDCD6BI BPDD C3B4DCBN AM C5D6B5 and has only D1 slack variables in the primal program. In Table1 we summarize the properties of the programs discussed above. As shown in the table, the advantage of using D0BE in the objective function is that the number of vari- ables in the dual problem in only a function of on CZ and D1 and does not depend on the number columns D0 in C5.... In PAGE 7: ... (24) can be solved using standard QP techniques. As shown in Table1 the dual program depends on D1CZ variables and has CZD1 B7 D1 con- straints all together. Converting the dual program in Eq.... ..."

Cited by 79

### Table 1: Summary of the sizes of the optimization problems for different norms. (See Appendix A for the definitions of the constraints in linear programming.)

"... In PAGE 7: ... In contrast, in our framework the confidence a73 a19a7a21 a2 a68 a48 a59a14a24 is com- pared to a95a98a97a14a99 a72 a9a8 a87 a59 a73 a19a5a21 a2 a68 a48 a72a27a24 and has only a32 slack variables in the primal program. In Table1 we summarize the properties of the programs discussed above. As shown in the table, the advantage of using a2a4a3 in the objective function is that the number of vari- ables in the dual problem in only a function of on a39 and a32 and does not depend on the number columns a2 in a48 .... In PAGE 8: ... (24) can be solved using standard QP techniques. As shown in Table1 the dual program depends on a32a110a39 variables and has a39a20a32 a5 a32 con- straints all together. Converting the dual program in Eq.... ..."