Antibody design is crucial for developing therapies against diseases such as cancer and viral infections. Recent deep generative models have significantly advanced computational antibody design, particularly in enhancing binding affinity to target antigens. However, beyond binding affinity, antibodies should exhibit other favorable biophysical properties such as non-antigen binding specificity and low self-association, which are important for antibody developability and clinical safety. To address this challenge, we propose AbNovo, a framework that leverages constrained preference optimization for multi-objective antibody design. First, we pre-train an antigen-conditioned generative model for antibody structure and sequence co-design. Then, we fine-tune the model using binding affinity as a reward while enforcing explicit constraints on other biophysical properties. Specifically, we model the physical binding energy with continuous rewards rather than pairwise preferences and explore a primal-and-dual approach for constrained optimization. Additionally, we incorporate a structure-aware protein language model to mitigate the issue of limited training data. Evaluated on independent test sets, AbNovo outperforms existing methods in metrics of binding affinity such as Rosetta binding energy and evolutionary plausibility, as well as in metrics for other biophysical properties like stability and specificity.