1 
Convex programming without constraint qualification : a study of Pareto optimalityFraklin, Martin Gordon. January 1975 (has links)
No description available.

2 
Solving discrete minimax problems with constraintsTurner, Bella Tobie January 1976 (has links)
No description available.

3 
A convex hull algorithm optimal for point sets in even dimensionsSeidel, Raimund January 1981 (has links)
Finding the convex hull of a finite set of points is important not only for practical applications but also for theoretical reasons: a number of geometrical problems, such as constructing Voronoi diagrams or intersecting hyperspheres, can be reduced to the convex hull problem, and a fast convex hull algorithm yields fast algorithms for these other problems.
This thesis deals with the problem of constructing the convex hull of a finite point set in R . Mathematical properties of convex hulls are developed, in particular, their facial structure, their representation, bounds on the number of faces, and the concept of duality. The main result of this thesis is an O(nlogn + n[(d+1)/2]) algorithm for the construction of the convex hull of n points in Rd. It is shown that this algorithm is worst case optimal for even d≥2. / Science, Faculty of / Computer Science, Department of / Graduate

4 
Continuous methods for convex programming and convex semidefinite programmingQian, Xun 07 August 2017 (has links)
In this thesis, we study several interior point continuous trajectories for linearly constrained convex programming (CP) and convex semidefinite programming (SDP). The continuous trajectories are characterized as the solution trajectories of corresponding ordinary differential equation (ODE) systems. All our ODE systems are closely related to interior point methods.. First, we propose and analyze three continuous trajectories, which are the solutions of three ODE systems for linearly constrained convex programming. The three ODE systems are formulated based on an variant of the affine scaling direction, the central path, and the affine scaling direction in interior point methods. The resulting solutions of the first two ODE systems are called generalized affine scaling trajectory and generalized central path, respectively. Under some mild conditions, the properties of the continuous trajectories, the optimality and convergence of the continuous trajectories are all obtained. Furthermore, we show that for the example of Gilbert et al. [Math. Program., { 103}, 6394 (2005)], where the central path does not converge, our generalized central path converges to an optimal solution of the same example in the limit.. Then we analyze two primal dual continuous trajectories for convex programming. The two continuous trajectories are derived from the primaldual pathfollowing method and the primaldual affine scaling method, respectively. Theoretical properties of the two interior point continuous trajectories are fully studied. The optimality and convergence of both interior point continuous trajectories are obtained for any interior feasible point under some mild conditions. In particular, with proper choice of some parameters, the convergence for both continuous trajectories does not require the strict complementarity or the analyticity of the objective function.. For convex semidefinite programming, four interior continuous trajectories defined by matrix differential equations are proposed and analyzed. Optimality and convergence of the continuous trajectories are also obtained under some mild conditions. We also propose a strategy to guarantee the optimality of the affine scaling algorithm for convex SDP.

5 
Convex programming without constraint qualification : a study of Pareto optimalityFraklin, Martin Gordon. January 1975 (has links)
No description available.

6 
Solving discrete minimax problems with constraintsTurner, Bella Tobie January 1976 (has links)
No description available.

7 
Decomposition methods for structured convex programmingHa, Cu Duong. January 1980 (has links)
Thesis (Ph. D.)University of WisconsinMadison, 1980. / Typescript. Vita. eContent providerneutral record in process. Description based on print version record. Includes bibliographical references (leaves 101106).

8 
Biconvex programming and deterministic and stochastic location allocation problemsSelim, Shokri Zaki 12 1900 (has links)
No description available.

9 
Algorithmtailored error bound conditions and the linear convergence rae of ADMMZeng, Shangzhi 30 October 2017 (has links)
In the literature, error bound conditions have been widely used for studying the linear convergence rates of various firstorder algorithms and the majority of literature focuses on how to sufficiently ensure these error bound conditions, usually posing more assumptions on the model under discussion. In this thesis, we focus on the alternating direction method of multipliers (ADMM), and show that the known error bound conditions for studying ADMM's linear convergence, can indeed be further weakened if the error bound is studied over the specific iterative sequence generated by ADMM. A socalled partial error bound condition, which is tailored for the specific ADMM's iterative scheme and weaker than known error bound conditions in the literature, is thus proposed to derive the linear convergence of ADMM. We further show that this partial error bound condition theoretically justifies the difference if the two primal variables are updated in different orders in implementing ADMM, which had been empirically observed in the literature yet no theory is known so far.

10 
On implementation of a selfdual embedding method for convex programming.January 2003 (has links)
by Cheng Tak Wai, Johnny. / Thesis (M.Phil.)Chinese University of Hong Kong, 2003. / Includes bibliographical references (leaves 5962). / Abstracts in English and Chinese. / Chapter 1  Introduction  p.1 / Chapter 2  Background  p.7 / Chapter 2.1  Selfdual embedding  p.7 / Chapter 2.2  Conic optimization  p.8 / Chapter 2.3  Selfdual embedded conic optimization  p.9 / Chapter 2.4  Connection with convex programming  p.11 / Chapter 2.5  Chapter summary  p.15 / Chapter 3  Implementation of the algorithm  p.17 / Chapter 3.1  The new search direction  p.17 / Chapter 3.2  Select the steplength  p.23 / Chapter 3.3  The multiconstraint case  p.25 / Chapter 3.4  Chapter summary  p.32 / Chapter 4  Numerical results on randomly generated problem  p.34 / Chapter 4.1  Singleconstraint problems  p.35 / Chapter 4.2  Multiconstraint problems  p.36 / Chapter 4.3  Running time and the size of the problem  p.39 / Chapter 4.4  Chapter summary  p.42 / Chapter 5  Geometric optimization  p.45 / Chapter 5.1  Geometric programming  p.45 / Chapter 5.1.1  Monomials and posynomials  p.45 / Chapter 5.1.2  Geometric programming  p.46 / Chapter 5.1.3  Geometric program in convex form  p.47 / Chapter 5.2  Conic transformation  p.48 / Chapter 5.3  Computational results of geometric optimization problem  p.50 / Chapter 5.4  Chapter summary  p.55 / Chapter 6  Conclusion  p.57

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