Optimal design and operation of complex chemical processes often require the solution of intricate dynamic optimization problems. A tailored simultaneous solution strategy based on multiple shooting and reduced SQP is presented. This reduced-space boundary value problem (BVP) approach allows an efficient and robust solution of multistage optimal control and design optimization problems for large, sparse DAE process models of index one. The current paper describes the theoretical aspects of the method. Utilizing the natural decomposition of the states into differential and algebraic variables, the structured NLP problem which results from the multiple shooting discretization of the optimization BVP is projected onto the reduced space of differential variables and control parameters. It is shown that this projection can be obtained very efficiently through direct computation of the reduced linearized constraint system via directional sensitivities. Like the original full-space BVP approach, the reduced-space formulation lends itself well to parallel computation. An implementation of the new strategy is provided by the modular optimal control package MUSCOD-II. Software aspects and applications are discussed in a second paper (Part II Software Aspects and Applications, 2002).