In this paper, we investigate the joint resource allocation and antenna selection algorithm design for uplink orthogonal frequency division multiple access (OFDMA) communication system. We propose a multi-objective optimization framework to strike a balance between spectral efficiency (SE) and energy efficiency (EE). The resource allocation design is formulated as a multi-objective optimization problem (MOOP), where the conflicting objective functions are linearly combined into a single objective function employing the weighted sum method. In order to develop an efficient solution, the majorization minimization (MM) approach is proposed where a surrogate function serves as a lower bound of the objective function. Then an iterative suboptimal algorithm is proposed to maximize the approximate objective function. Numerical results unveil an interesting tradeoff between the considered conflicting system design objectives and reveal the improved EE and SE facilitated by the proposed transmit antenna selection in OFDMA systems.