A power supply configured to supply power to a capacitive load, the power supply comprising: a converter configured to convert alternating current from an alternating-current power source into direct current; an inverter configured to convert the direct current from the converter into alternating current; a resonant transformer configured to boost the alternating current from the inverter, and output the boosted alternating current to the capacitive load; a detector configured to detect output frequency or output current and output voltage of the alternating current output to the capacitive load; and a controller configured to control the inverter, wherein the controller is configured to: calculate output power of the alternating current output to the capacitive load, based on a detection result of the detector; characterized in that the controller is further configured to: perform a frequency specifying process wherein the output frequency is adjusted within a predetermined frequency search range and the output voltage is adjusted within a predetermined voltage search range, and specifying, as a frequency target value, a minimum value of the output frequency with which the output power reaches predetermined output power that is greater than or equal to a target output power; and perform a voltage specifying process of controlling the inverter wherein the output voltage is adjusted within the predetermined voltage search range while maintaining the output frequency at said frequency target value, and specifying, as a voltage target value, a value of the output voltage with which the output power is the target output power; and control the inverter to supply power while maintaining the output frequency and the output voltage at their respective target values. a converter configured to convert alternating current from an alternating-current power source into direct current; an inverter configured to convert the direct current from the converter into alternating current; a resonant transformer configured to boost the alternating current from the inverter, and output the boosted alternating current to the capacitive load; a detector configured to detect output frequency or output current and output voltage of the alternating current output to the capacitive load; and a controller configured to control the inverter, wherein the controller is configured to: calculate output power of the alternating current output to the capacitive load, based on a detection result of the detector; characterized in that the controller is further configured to: perform a frequency specifying process wherein the output frequency is adjusted within a predetermined frequency search range and the output voltage is adjusted within a predetermined voltage search range, and specifying, as a frequency target value, a minimum value of the output frequency with which the output power reaches predetermined output power that is greater than or equal to a target output power; and perform a voltage specifying process of controlling the inverter wherein the output voltage is adjusted within the predetermined voltage search range while maintaining the output frequency at said frequency target value, and specifying, as a voltage target value, a value of the output voltage with which the output power is the target output power; and control the inverter to supply power while maintaining the output frequency and the output voltage at their respective target values. calculate output power of the alternating current output to the capacitive load, based on a detection result of the detector; characterized in that the controller is further configured to: perform a frequency specifying process wherein the output frequency is adjusted within a predetermined frequency search range and the output voltage is adjusted within a predetermined voltage search range, and specifying, as a frequency target value, a minimum value of the output frequency with which the output power reaches predetermined output power that is greater than or equal to a target output power; and perform a voltage specifying process of controlling the inverter wherein the output voltage is adjusted within the predetermined voltage search range while maintaining the output frequency at said frequency target value, and specifying, as a voltage target value, a value of the output voltage with which the output power is the target output power; and control the inverter to supply power while maintaining the output frequency and the output voltage at their respective target values. perform a frequency specifying process wherein the output frequency is adjusted within a predetermined frequency search range and the output voltage is adjusted within a predetermined voltage search range, and specifying, as a frequency target value, a minimum value of the output frequency with which the output power reaches predetermined output power that is greater than or equal to a target output power; and perform a voltage specifying process of controlling the inverter wherein the output voltage is adjusted within the predetermined voltage search range while maintaining the output frequency at said frequency target value, and specifying, as a voltage target value, a value of the output voltage with which the output power is the target output power; and control the inverter to supply power while maintaining the output frequency and the output voltage at their respective target values.