Integer programming and combinatorial optimization are increasingly central to the design of robust systematic trading and portfolio construction frameworks. As markets demand higher capital efficiency, tighter risk budgets, and execution-aware allocation, quant teams are moving beyond closed-form heuristics and embracing discrete optimization methods to model the real constraints of trading systems.

This book provides a practical, finance-focused guide to mixed-integer optimization for allocation, execution, and systematic decision-making. Readers will learn how to encode market frictions, turnover limits, transaction costs, liquidity constraints, sector exposures, and nonlinear objectives into tractable optimization problems that directly reflect modern portfolio engineering realities.

Developed for quantitative analysts, portfolio managers, and algorithmic traders, the material bridges the gap between academic integer programming theory and high-performance implementation inside systematic workflows. Through worked examples and trading-oriented case studies, the book demonstrates how combinatorial structures appear naturally in portfolio construction, order scheduling, basket execution, and risk overlays-and how these structures can be efficiently optimized with modern solvers.

Core topics include:

- Mixed-integer linear & quadratic models for systematic strategies
- Discrete allocation under liquidity, turnover, and risk constraints
- Execution scheduling and basket optimization
- Constraint-driven risk modeling and factor exposure alignment
- Combinatorial search, heuristics, and relaxation techniques
- Solver selection, performance considerations, and workflow integration
- Practical implementation patterns for production trading systems

By the end, readers will be equipped to design discrete optimization components that integrate directly into quant trading pipelines, strategy research platforms, and PM workflows, turning combinatorial problems into systematic trading edges.

Ideal for systematic traders, quant developers, risk teams, PMs, and researchers working in portfolio optimization, algorithmic trading, and execution-aware strategy engineering.