Applications of convex optimization in naval engineering

Convex optimization is a class of nonlinear optimization with many useful theoretical and computational properties. The global optimum can be computed very efficiently, even for largescale problems. The numerical solvers for convex optimization require no initial guesses or parameter tuning. This thesis focuses on applying convex optimization to model several important nonlinear problems in naval engineering. Chapter 2 presents the theoretical background for this work. The thesis is written as a collection of articles, and the remaining chapters summarize the results of the articles. Chapter 3 formulates conceptual-stage marine vessel design problems as geometric programs. Although geometric programs are nonconvex, they can be reformulated as convex problems with no sacrifice in fidelity. This reformulation creates a novel possibility for fast systemlevel design optimization. Chapter 4 considers the problem of generating time-optimal trajectories for energy-limited surface vessels. The convexification techniques developed in this chapter lay the path for employing computationally robust convex optimization methods in a real-time environment with strict runtime and reliability requirements. Chapters 5 and 6 model problems that include discrete decisions. The first problem deals with lifetime fuel and power system selection, and the second problem involves hybrid power source energy management.