It's more acceptable in everyday writing. But for business and academic writing, reword your thought and write it without "Anyway" as a sentence beginning. "Anyway" is a fluff or filler word, similar to saying "you know". It often is not needed.
Informal:
I tried to tell the boy not to run on the ice but he wouldn't listen. Anyway, he fell, broke his leg, and I called the ambulance.
Formal:
I tried to tell the boy not to run on the ice but he wouldn't listen. He fell, broke his leg, and I called the ambulance.
Anyway, I was hopeful that you would call soon.
I can't get the Prize, anyway. You are quite a prize.
I'm not sure why you wouldn't begin a sentence with it. It's just a word. All of those grammar rules they taught in school are wrong anyway. You can start any sentence with any word; you just have to follow the rules for starting the sentence that way. Why? Because if you didn't follow the rules, then you would end up with a bad sentence! You're perfectly allowed to put 'you're' at the start of a sentence in any case.
No, you cannot start a sentence with "no" unless you need to do so. No reason exists not to start a sentence with that word, as you can see. No one will care if you do start a sentence with it.
When you need a command sentence for sillier. IT can not start with word that has I in iy.
"Well, of course you can." The word here has no specific meaning, it is more of a mild interjection. The word "anyway" is similarly used as a throw-away word in conversations. Better would be an affirmation / negation such as "Yes", "No", or an emotional "Gee whiz".
Anyway.
I can't get the Prize, anyway. You are quite a prize.
you can do your art project anyway you want
can you start a sentence using the word phishing?
No. There is no word in English that cannot start a sentence.
It doesn't matter how much it costs, I don't have any money anyway.
no!
No, you cannot start a sentence with "no" unless you need to do so. No reason exists not to start a sentence with that word, as you can see. No one will care if you do start a sentence with it.
I'm not sure why you wouldn't begin a sentence with it. It's just a word. All of those grammar rules they taught in school are wrong anyway. You can start any sentence with any word; you just have to follow the rules for starting the sentence that way. Why? Because if you didn't follow the rules, then you would end up with a bad sentence! You're perfectly allowed to put 'you're' at the start of a sentence in any case.
What sentence would you like?
When it is at the start of a sentence.
To have courage is to fear something but do it anyway.