I. INTRODUCTION
A. Evolution of Wireless Cellular Communication Systems: From 1G to 6G
C. Goals of the Paper
D. Structure of the Paper
II. OPTIMIZATION PROBLEMS IN WIRELESS COMMUNICATIONS: STRUCTURES AND CHALLENGES
A. Optimization Problems in Wireless Communications
B. Challenges from the Optimization Perspective
C. Structural Properties of Optimization Problems
III. STRUCTURED NONCONVEX OPTIMIZATION
IV. PROBLEM-SPECIFIC GLOBAL OPTIMIZATION
V. OPTIMIZATION IN DISTRIBUTED NETWORKS
A. Decomposition Methods
B. Federated Learning in Wireless Edge Networks
VI. OPTIMIZATION VIA LEARNING
VII. LEARNING-BASED OPTIMIZATION WITHOUT EXPLICIT CHANNEL ESTIMATION
VIII. OPEN PROBLEMS AND RESEARCH DIRECTIONS
A. Open Problems
B. Research Directions
IX. CONCLUSION