The administration yesterday released a midyear economic review that forecasts a beginning of recovery in the latter half of this year and 4.4 percent growth next year. It also foresees unemployment falling to 8 percent and inflation to 7.2 percent by the end of next year.

Except for the inflation forecast, most of the projections represent sharp improvements over current economic conditions. They are considered optimistic not only by private forecasters but by the Congressional Budget Office and many administration economic officials.

Although the midyear review is meant to be the latest official word on the economic outlook and budget totals for the next five years, a top administration official told reporters that the review's "assumptions" about economic growth, inflation and other factors are not the result of a thorough update on the economy.

Rather, the administration revised only the 1982 economic projections. The forecasts for 1983 to 1987 are unchanged from those given Congress about five months ago. Since then the picture has worsened.

The revised 1982 figures project a 9.1 percent unemployment rate at the end of the year and a 4.8 percent inflation rate. The output of goods and services is expected to fall 0.7 percent.

The official said the forecast contained few revisions because the document was designed to keep Congress on the course outlined in the compromise budget and not confuse the debate over $77 billion worth of savings with a host of "new" numbers.

The Office of Management and Budget also said it anticipates that the federal budget deficit will be $115 billion in the 1983 spending year that starts Oct. 1, $13 billion more the compromise budget called for last spring.

The $115 billion deficit, however, is based on the economic assumptions embodied in the midyear review. It is sharply lower than the $140 billion to $160 billion deficit projected by the CBO earlier this week, a deficit projection that is in line with many private forecasts.

The 1983 budget and its optimistic tones sparked internal disputes within the administration and, sources said, triggered the resignation of Council of Economic Advisers member Jerry Jordan and vexed chairman Murray Weidenbaum, whose resignation was announced last week. Treasury Secretary Donald T. Regan, who normally could have been expected to attend the budget briefing, did not.

Yesterday the high-ranking official, who requested anonymity, declined to embrace the entire forecast, but said what is "more important is to get policy changes made by Congress , then re-estimate later." He said the administration will undertake a thorough economic review in the fall before sending its 1984 budget proposal to Congress in January.

The official said the Reagan administration "absolutely" adheres to the compromise 1983 budget that envisions $77 billion in deficit "reductions"--including spending cuts, tax increases and other "savings"--and trims $8.6 billion from the president's proposed defense spending and adds $4.5 billion to social programs.

Neverthless, the administration official said, President Reagan does not feel bound to the spending targets envisioned for 1984 and 1985 in the budget resolution and may propose higher defense spending outlays and further domestic spending cuts in the 1984 budget he will present to Congress early next year.

The review includes about $17 billion in defense spending for 1984 and 1985 that was rejected by Congress in the budget resolution.

Although the official often danced away from the economic forecasts embraced in the resolution--and, by implication, from some of the budget projections such as the $115 billion deficit that are based on those economic assumptions--he also argued that the economic assumptions are not that far out of line.