### Table 6 Unconstrained maximum of the quadratic programming problem.

"... In PAGE 32: ... Now (69) restricted to (i; j) can be rewritten as follows: maximize 8 gt; lt; gt; : ?12 i ? i j ? j gt; Kii Kij Kji Kjj i ? i j ? j +vi( i ? i ) + vj( j ? j) ? quot;( i + i + j + j) subject to ( i ? i ) + ( j ? j) = i; i ; j; j 2 [0; C] (81) Next one has to eliminate j; j by exploiting the summation constraint. Ig- noring terms independent of ( ) i one obtains10 maximize ?12( i ? i )2(Kii + Kjj ? 2Kij) ? quot;( i + i )(1 ? s) +( i ? i )(vi ? vj ? (Kij ? Kjj)) subject to ( ) i 2 [L( ); H( )]: (82) The unconstrained maximum of (82) with respect to i or i can be found in Table6 . Here the shorthand := Kii + Kjj ? 2Kij is used.... ..."

### Table 2: Sizes of norm minimization problems, SDP relaxation of quadratic programs with box constraints, SDP relaxation of the maximum cut problems, and SDP relaxation of graph partition problems.

2004

"... In PAGE 12: ...e., norm minimization problems, SDP relaxation of quadratic programs with box constraints, SDP relaxation of max-cut problems over lattice graphs, and SDP relaxation of graph partitioning problems, are shown at Table2 . The original formulation of graph partitioning problems gives a dense aggregate sparsity pattern not allowing us to use the conversion method, and therefore we previously applied an appropriate congruent transformation [8, Section 6] to them.... ..."

### Table 3: Numerical results on norm minimization problems, SDP relaxation of quadratic programs with box constraints, SDP relaxation of the maximum cut problems, and SDP relaxation of graph partition problems for SDPA 6.00 at computer A.

2004

### Table 4: Numerical results on norm minimization problems, SDP relaxation of quadratic programs with box constraints, SDP relaxation of the maximum cut problems, and SDP relaxation of graph partition problems for SDPA 6.00 at computer B.

2004

### Table 5: Numerical results on norm minimization problems, SDP relaxation of quadratic programs with box constraints, SDP relaxation of the maximum cut problems, and SDP relaxation of graph partition problems for SDPT3 3.02 at computer A.

2004

### Table 6: Numerical results on norm minimization problems, SDP relaxation of quadratic programs with box constraints, SDP relaxation of the maximum cut problems, and SDP relaxation of graph partition problems for SDPT3 3.02 at computer B.

2004

### Table 1 The di erent types of optimization problems treated in TOMLAB. probType Number Description of the type of problem uc 1 Unconstrained optimization (incl. bound constraints). qp 2 Quadratic programming.

"... In PAGE 3: ...rowing. This motivates a well-de ned naming convention and design. TOMLAB solves a number of di erent types of optimization problems. Currently, we have de ned the types listed in Table1 . The global variable prob- Type is the current type to be solved.... In PAGE 3: ... The global variable prob- Type is the current type to be solved. An optimization solver is de ned to be of type solvType, where solvType is any of the probType entries in Table1 . It is clear that a solver of a certain solvType is able to solve a problem de ned to be of... ..."

### Table 1: The di erent types of optimization problems treated in NLPLIB TB. probType Number Description of the type of problem uc 1 Unconstrained optimization (incl. bound constraints). qp 2 Quadratic programming.

1999

"... In PAGE 3: ... The global variable probType is the current type to be solved. An optimization solver is de ned to be of type solvType, where solvType is any of the probType entries in Table1 . It is clear that a solver of a certain solvType is able to solve a problem de ned to be of another type.... In PAGE 19: ...65 Table1 0: Information stored in the structure Prob.NTS Field Description SepAlg If SepAlg = 1, use separable non linear least squares formulation, default 0.... In PAGE 19: ... alpha Weights in autoregressive models. Table1 1: Information stored in the structure Prob.PartSep Field Description pSepFunc Number of partially separable functions.... In PAGE 20: ...66 Table1 2: Information stored in the structure Prob.GLOBAL Field Description iterations Number of iterations, default 50.... In PAGE 20: ... t t(i) is the total number of splits along dimension i. Table1 3: Information stored in the structure Prob.USER Field Description f Name of m- le computing the objective function f(x).... In PAGE 21: ...67 Table1 4: Information stored in the structure Prob.optParam.... In PAGE 22: ...68 Table1 5: Information stored in the global Matlab structure Result. Field Description Iter Number of major iterations.... In PAGE 23: ...69 Table1 6: The state variable xState for the variable. Value Description 0 A free variable.... In PAGE 23: ... 3 Variable is xed, lower bound is equal to upper bound. Table1 7: The state variable bState for each linear constraint. Value Description 0 Inactive constraint.... In PAGE 23: ... 3 Linear equality constraint. Table1 8: Information stored in the structure Result.GLOBAL Field Description C Matrix with all rectangle centerpoints in original coordinates.... In PAGE 23: ... t t(i) is the total number of splits along dimension i. Table1 9: Matlab Optimization toolbox routines with a TOMLAB interface. Function Type of problem solved constr Constrained minimization.... ..."

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