of SAT Algorithms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7:3 3. Preliminaries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . IV 4. Complete Algorithms and Incomplete Algorithms . . . . . . . . . . . . . . . . . . . . . . . . . . 81 5. Optimization: An Iterative Refinement Process . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86 6. Local Search Algorithms for SAT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89 7. Global Optimization Algorithms for SAT Problem . . . . . . . . . . . . . . . . . . . . . . . . 106 8. Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 137 9. Future Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 140 10. Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 141 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 143 Ergodic Convergence in Proximal Point Algorithms with Bregman Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 155 Osman Guier 1. Introduction . . . : . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 155 2. Convergence for Function Minimization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 158 3. Convergence for Arbitrary Maximal Monotone Operators . . . . . . . . . . . . . . . . . 161 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 163 Adding and Deleting Constraints in the Logarithmic

Preface. Scheduling Multiprocessor Flow Shops; Bo Chen. The k-Walk Polyhedron; C.R. Coullard, A.B. Gamble, Jin Liu. Two Geometric Optimization Problems; B. Dasgupta, V. Roychowdhury. A Scaled Gradient Projection Algorithm for Linear Complementarity Problems; Jiu Ding. A Simple Proof for a Result of Ollerenshaw on Steiner Trees; Xiufeng Du, Ding-Zhu Du, Biao Gao, Lixue Qü. Optimization Algorithms for the Satisfiability (SAT) Problem; Jun Gu. Ergodic Convergence in Proximal Point Algorithms with Bregman Functions; O. Güler. Adding and Deleting Constraints in the Logarithmic Barrier Method for LP; D. den Hertog, C. Roos, T. Terlaky. A Projection Method for Solving Infinite Systems of Linear Inequalities; Hui Hu. Optimization Problems in Molecular Biology; Tao Jiang, Ming Li. A Dual Affine Scaling Based Algorithm for Solving Linear Semi-Infinite Programming Problems; Chih-Jen Lin, Shu-Cherng Fang, Soon-Yi Wu. A Genuine Quadratically Convergent Polynomial Interior Point Algorithm for Linear Programming; Zhi-Quan Luo, Yinyu Ye. A Modified Barrier Function Method for Linear Programming; M.R. Osborne. A New Facet Class and a Polyhedral Method for the Three-Index Assignment Problem; Liqun Qi, E. Balas, G. Gwan. A Finite Simplex-Active-Set Method for Monotropic Piecewise Quadratic Programming; R.T. Rockafellar, Jie Sun. A New Approach in the Optimization of Exponential Queues; S.H. Xu. The Euclidean Facilities Location Problem; Guoliang Xue, Changyu Wang. Optimal Design of Large-Scale Opencut Coal Mine System; Dezhuang Yang. On the Strictly Complementary Slackness Relation in Linear Programming; Shuzhong Zhang. Analytical Properties of the Central Trajectory in Interior Point Methods; Gongyun Zhao,Jishan Zhu. The Approximation of Fixed Points of Robust Mappings; Quan Zheng, Deming Zhuang.