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  • 1
    Monograph available for loan
    Monograph available for loan
    Data, models, and decisions : The fundamentals of management science (2000)
    South-Western Publishing Company : Cincinnati / OH
    Details Availability
    Call number: PIK M 370-02-0071
    Type of Medium: Monograph available for loan
    Pages: 530 p. + CD
    ISBN: 0538859067
    Location: A 18 - must be ordered
    Branch Library: PIK Library
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  • 2
    Electronic Resource
    Electronic Resource
    Electron-impact ionization cross sections of the SiF3 free radical (1988)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 89 (1988), S. 4035-4041 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: Absolute cross sections for electron-impact ionization of the SiF3 free radical from threshold to 200 eV are presented for formation of the parent SiF+3 ion and the fragment SiF+2, SiF+, and Si+ ions. A 3 keV beam of SiF3 is prepared by near-resonant charge transfer of SiF+3 with 1,3,5-trimethylbenzene. The beam contains only ground electronic state neutral radicals, but with as much as 1.5 eV of vibrational energy. The absolute cross section for formation of the parent ion at 70 eV is 0.67±0.09 A(ring)2. At 70 eV the formation of SiF+2 is the major process, having a cross section 2.51±0.02 times larger than that of the parent ion, while the SiF+ fragment has a cross section 1.47±0.08 times larger than the parent. Threshold measurements show that ion pair dissociation processes make a significant contribution to the formation of positively charged fragment ions.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.454836
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  • 3
    Electronic Resource
    Electronic Resource
    Electron impact ionization cross sections of SiF2 (1988)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 89 (1988), S. 4042-4047 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: Absolute cross sections are measured for electron impact ionization and dissociative ionization of SiF2 from threshold to 200 eV. A fast (3 keV) neutral beam of SiF2 is formed by charge transfer neutralization of SiF+2 with Xe; it is primarily in the ground electronic state with about 10% in the metastable first excited electronic state (a˜ 3B1). The absolute cross section for ionization of the ground state by 70 eV electrons to the parent SiF+2 is 1.38±0.18 A(ring)2. Formation of SiF+ is the major process with a cross section at 70 eV of 2.32±0.30 A(ring)2. The cross section at 70 eV for formation of the Si fragment ion is 0.48±0.08 A(ring)2. Ion pair production contributes a significant fraction of the positively charged fragment ions.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.454837
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  • 4
    Electronic Resource
    Electronic Resource
    Absolute cross sections for electron-impact ionization and dissociative ionization of the SiF free radical (1988)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 88 (1988), S. 823-829 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: Absolute cross sections for electron-impact ionization of the SiF free radical from threshold to 200 eV are presented for formation of the parent SiF+ ion and the fragment Si+ and F+ ions. A fast beam of SiF is prepared by charge transfer neutralization of an SiF+ beam. The radicals form in the ground electronic state and predominantly in their ground vibrational state, as shown by agreement of the measured ionization threshold with the ionization potential. The absolute cross section for SiF→SiF+ at 70 eV is 3.90±0.32 A(ring)2. The ratio of cross sections for formation of Si+ to that for SiF+ at 70 eV is 0.528±0.024; the ratio for formation of F+ to that of SiF+ is 0.060±0.008. The observed threshold energy for Si+ formation indicates the importance of ion pair formation SiF→Si++F−. Breaks in the cross section at 14.3 and 17 eV are assigned as dissociative ionization thresholds.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.454161
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  • 5
    Electronic Resource
    Electronic Resource
    Some characterizations and properties of the “distance to ill-posedness” and the condition measure of a conic linear system (1999)
    Springer
    Mathematical programming 86 (1999), S. 225-260 
    Details
    ISSN: 1436-4646
    Keywords: Key words: complexity of linear programming – infinite programming – interior point methods – conditioning –error analysis Mathematics Subject Classification (1991): 90C, 90C05, 90C60
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract. A conic linear system is a system of the form¶P(d): find x that solves b - Ax∈C Y , x∈C X ,¶ where C X and C Y are closed convex cones, and the data for the system is d=(A,b). This system is“well-posed” to the extent that (small) changes in the data (A,b) do not alter the status of the system (the system remains solvable or not). Renegar defined the “distance to ill-posedness”, ρ(d), to be the smallest change in the data Δd=(ΔA,Δb) for which the system P(d+Δd) is “ill-posed”, i.e., d+Δd is in the intersection of the closure of feasible and infeasible instances d’=(A’,b’) of P(·). Renegar also defined the “condition measure” of the data instance d as C(d):=∥d∥/ρ(d), and showed that this measure is a natural extension of the familiar condition measure associated with systems of linear equations. This study presents two categories of results related to ρ(d), the distance to ill-posedness, and C(d), the condition measure of d. The first category of results involves the approximation of ρ(d) as the optimal value of certain mathematical programs. We present ten different mathematical programs each of whose optimal values provides an approximation of ρ(d) to within certain constants, depending on whether P(d) is feasible or not, and where the constants depend on properties of the cones and the norms used. The second category of results involves the existence of certain inscribed and intersecting balls involving the feasible region of P(d) or the feasible region of its alternative system, in the spirit of the ellipsoid algorithm. These results roughly state that the feasible region of P(d) (or its alternative system when P(d) is not feasible) will contain a ball of radius r that is itself no more than a distance R from the origin, where the ratio R/r satisfies R/r≤c 1 C(d), and such that r≥ and R≤c 3 C(d), where c 1,c 2,c 3 are constants that depend only on properties of the cones and the norms used. Therefore the condition measure C(d) is a relevant tool in proving the existence of an inscribed ball in the feasible region of P(d) that is not too far from the origin and whose radius is not too small.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/s10107990063a
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  • 6
    Electronic Resource
    Electronic Resource
    On the complexity of four polyhedral set containment problems (1985)
    Springer
    Mathematical programming 33 (1985), S. 139-145 
    Details
    ISSN: 1436-4646
    Keywords: Computational Complexity ; NP-Complete ; Linear Program ; Polyhedron ; Cell
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract A nonempty closed convex polyhedronX can be represented either asX = {x: Ax ⩽b}, where (A, b) are given, in which caseX is called anH-cell, or in the formX = {x: x = Uλ + Vμ, Σλ j = 1,λ ⩾ 0,μ ⩾ 0}, where (U, V) are given, in which caseX is called aW-cell. This note discusses the computational complexity of certain set containment problems. The problems of determining if $$X \nsubseteq Y$$ , where (i)X is anH-cell andY is a closed solid ball, (ii)X is anH-cell andY is aW-cell, or (iii)X is a closed solid ball andY is aW-cell, are all shown to be NP-complete, essentially verifying a conjecture of Eaves and Freund. Furthermore, the problem of determining whether there exists an integer point in aW-cell is shown to be NP-complete, demonstrating that regardless of the representation ofX as anH-cell orW-cell, this integer containment problem is NP-complete.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01582241
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  • 7
    Electronic Resource
    Electronic Resource
    Polynomial-time algorithms for linear programming based only on primal scaling and projected gradients of a potential function (1991)
    Springer
    Mathematical programming 51 (1991), S. 203-222 
    Details
    ISSN: 1436-4646
    Keywords: Linear program ; polynomial time bound ; affine scaling ; interior-point algorithm
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract This paper presents extensions and further analytical properties of algorithms for linear programming based only on primal scaling and projected gradients of a potential function. The paper contains extensions and analysis of two polynomial-time algorithms for linear programming. We first present an extension of Gonzaga's O(nL) iteration algorithm, that computes dual variables and does not assume a known optimal objective function value. This algorithm uses only affine scaling, and is based on computing the projected gradient of the potential function $$q\ln (x^T s) - \sum\limits_{j = 1}^n {\ln (x_j )} $$ wherex is the vector of primal variables ands is the vector of dual slack variables, and q = n + $$\sqrt n $$ . The algorithm takes either a primal step or recomputes dual variables at each iteration. We next present an alternate form of Ye's O( $$\sqrt n $$ L) iteration algorithm, that is an extension of the first algorithm of the paper, but uses the potential function $$q\ln (x^T s) - \sum\limits_{j = 1}^n {\ln (x_j ) - \sum\limits_{j - 1}^n {\ln (s_j )} } $$ where q = n + $$\sqrt n $$ . We use this alternate form of Ye's algorithm to show that Ye's algorithm is optimal with respect to the choice of the parameterq in the following sense. Suppose thatq = n + n t wheret⩾0. Then the algorithm will solve the linear program in O(n r L) iterations, wherer = max{t, 1 − t}. Thus the value oft that minimizes the complexity bound ist = 1/2, yielding Ye's O( $$\sqrt n $$ L) iteration bound.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01586933
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  • 8
    Electronic Resource
    Electronic Resource
    A potential-function reduction algorithm for solving a linear program directly from an infeasible “warm start” (1991)
    Springer
    Mathematical programming 52 (1991), S. 441-466 
    Details
    ISSN: 1436-4646
    Keywords: Linear program ; potential function ; shifted barrier ; interior point algorithm ; polynomial time bound
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract This paper develops an algorithm for solving a standard-form linear program directly from an infeasible “warm start”, i.e., directly from a given infeasible solution $$\hat x$$ that satisfies $$A\hat x = b$$ but $$\hat x \ngeqslant 0$$ . The algorithm is a potential function reduction algorithm, but the potential function is somewhat different than other interior-point method potential functions, and is given by $$F(x,B) = q\ln (c^T x - B) - \sum\limits_{j = 1}^n {\ln (x_j + h_j (c^T x - B))}$$ where $$q = n + \sqrt n$$ is a given constant,h is a given strictly positive shift vector used to shift the nonnegativity constaints, andB is a lower bound on the optimal value of the linear program. The duality gapc T x − B is used both in the leading term as well as in the barrier term to help shift the nonnegativity constraints. The algorithm is shown under suitable conditions to achieve a constant decrease in the potential function and so achieves a constant decrease in the duality gap (and hence also in the infeasibility) in O(n) iterations. Under more restrictive assumptions regarding the dual feasible region, this algorithm is modified by the addition of a dual barrier term, and will achieve a constant decrease in the duality gap (and in the infeasibility) in $$O(\sqrt n )$$ iterations.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01582900
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  • 9
    Electronic Resource
    Electronic Resource
    Projective transformations for interior-point algorithms, and a superlinearly convergent algorithm for the w-center problem (1993)
    Springer
    Mathematical programming 58 (1993), S. 385-414 
    Details
    ISSN: 1436-4646
    Keywords: Analytic center ; w-center ; projective transformation ; linear program ; ellipsoid ; barrier penalty ; Newton method
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract The purpose of this study is to broaden the scope of projective transformation methods in mathematical programming, both in terms of theory and algorithms. We start by generalizing the concept of the analytic center of a polyhedral system of constraints to the w-center of a polyhedral system, which stands for weighted center, where there is a positive weight on the logarithmic barrier term for each inequality constraint defining the polyhedronX. We prove basic results regarding contained and containing ellipsoids centered at the w-center of the systemX. We next shift attention to projective transformations, and we exhibit an elementary projective transformation that transforms the polyhedronX to another polyhedronZ, and that transforms the current interior point to the w-center of the transformed polyhedronZ. We work throughout with a polyhedral system of the most general form, namely both inequality and equality costraints. This theory is then applied to the problem of finding the w-center of a polyhedral systemX. We present a projective transformation algorithm, which is an extension of Karmarkar's algorithm, for finding the w-center of the systemX. At each iteration, the algorithm exhibits either a fixed constant objective function improvement, or converges superlinearly to the optimal solution. The algorithm produces upper bounds on the optimal value at each iteration. The direction chosen at each iteration is shown to be a positively scaled Newton direction. This broadens a result of Bayer and Lagarias regarding the connection between projective transformation methods and Newton's method. Furthermore, the algorithm specializes to Vaidya's algorithm when used with a line-search, and so shows that Vaidya's algorithm is superlinearly convergent as well. Finally, we show how the algorithm can be used to construct well-scaled containing and contained ellipsoids at near-optimal solutions to the w-center problem.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01581277
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  • 10
    Electronic Resource
    Electronic Resource
    Condition number complexity of an elementary algorithm for computing a reliable solution of a conic linear system (2000)
    Springer
    Mathematical programming 88 (2000), S. 451-485 
    Details
    ISSN: 1436-4646
    Keywords: Key words: complexity of convex programming – conditioning – error analysis ; Mathematics Subject Classification (1991): 90C, 90C05, 90C60
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract. A conic linear system is a system of the form¶¶(FP d )Ax=b¶x∈C X ,¶¶where A:X?Y is a linear operator between n- and m-dimensional linear spaces X and Y, b∈Y, and C X ⊂X is a closed convex cone. The data for the system is d=(A,b). This system is “well-posed” to the extent that (small) changes in the data d=(A,b) do not alter the status of the system (the system remains feasible or not). Renegar defined the “distance to ill-posedness,”ρ(d), to be the smallest change in the data Δd=(ΔA,Δb) needed to create a data instance d+Δd that is “ill-posed,” i.e., that lies in the intersection of the closures of the sets of feasible and infeasible instances d ′=(A ′,b ′) of (FP(·)). Renegar also defined the condition number ?(d) of the data instance d as the scale-invariant reciprocal of ρ(d) : ?(d)= .¶In this paper we develop an elementary algorithm that computes a solution of (FP d ) when it is feasible, or demonstrates that (FP d ) has no solution by computing a solution of the alternative system. The algorithm is based on a generalization of von Neumann’s algorithm for solving linear inequalities. The number of iterations of the algorithm is essentially bounded by¶¶O(  ?(d)2ln(?(d)))¶¶where the constant depends only on the properties of the cone C X and is independent of data d. Each iteration of the algorithm performs a small number of matrix-vector and vector-vector multiplications (that take full advantage of the sparsity of the original data) plus a small number of other operations involving the cone C X . The algorithm is “elementary” in the sense that it performs only a few relatively simple computations at each iteration.¶The solution of the system (FP d ) generated by the algorithm has the property of being “reliable” in the sense that the distance from to the boundary of the cone C X , dist( ,∂C X ), and the size of the solution, ∥ ∥, satisfy the following inequalities:¶¶∥ ∥≤c 1?(d),dist( ,∂C X )≥c 2 , and ≤c 3?(d),¶¶where c 1, c 2, c 3 are constants that depend only on properties of the cone C X and are independent of the data d (with analogous results for the alternative system when the system (FP d ) is infeasible).
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/s101070000136
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