Just to confirm (to some extent) what Jean Logeart said in his answer: When adding a trivial main that calls both methods, as in 
class MaxOpt
{
    public static void main(String args[])
    {
        for (int i=0; i<100000; i++)
        {
            runTests();
        }
    }
    private static void runTests()
    {
        test0();
        test1();
    }
    private static final int n = 10000;
    public static void test0(){
        int m = 0;
        for(int i = 0; i < n; ++i){
            m = Math.max(i, m);
        }
    }
    public static void test1(){
        int m = 0;
        for(int i = 0; i < n; ++i){
            m = ((i >= m) ? i : m);
        }
    }
}
And running it in a hotspot disassembler VM with 
-XX:+UnlockDiagnosticVMOptions -XX:+TraceClassLoading -XX:+LogCompilation -XX:+PrintInlining -XX:+PrintAssembly
then (on Win7/64 with Java 1.8.0_92) the final machine code of the test0 method will be
Decoding compiled method 0x0000000002925510:
Code:
[Entry Point]
[Verified Entry Point]
[Constants]
  # {method} {0x000000001bd10458} 'test0' '()V' in 'MaxOpt'
  #           [sp+0x20]  (sp of caller)
  0x0000000002925640: sub    $0x18,%rsp
  0x0000000002925647: mov    %rbp,0x10(%rsp)    ;*synchronization entry
                        ; - MaxOpt::test0@-1 (line 20)
  0x000000000292564c: add    $0x10,%rsp
  0x0000000002925650: pop    %rbp
  0x0000000002925651: test   %eax,-0x26f5657(%rip)        # 0x0000000000230000
                        ;   {poll_return}
  0x0000000002925657: retq   
  0x0000000002925658: hlt    
  0x0000000002925659: hlt    
  0x000000000292565a: hlt    
  0x000000000292565b: hlt    
  0x000000000292565c: hlt    
  0x000000000292565d: hlt    
  0x000000000292565e: hlt    
  0x000000000292565f: hlt    
[Exception Handler]
  ...   
Yes, it basically does nothing. 
Surprisingly, for test1, the JIT obviously does some odd loop unrolling, but does not seem to detect that the method is useless and side-effect-free (it could be optimized away, but it is not)
The resulting assembly is rather huge....:
Decoding compiled method 0x0000000002926290:
Code:
[Entry Point]
[Verified Entry Point]
[Constants]
  # {method} {0x000000001bd103a8} 'runTests' '()V' in 'MaxOpt'
  #           [sp+0x30]  (sp of caller)
  0x00000000029263c0: mov    %eax,-0x6000(%rsp)
  0x00000000029263c7: push   %rbp
  0x00000000029263c8: sub    $0x20,%rsp         ;*synchronization entry
                        ; - MaxOpt::runTests@-1 (line 13)
  0x00000000029263cc: xor    %r8d,%r8d
  0x00000000029263cf: mov    $0x1,%r11d
  0x00000000029263d5: data32 data32 nopw 0x0(%rax,%rax,1)
                        ;*iload_1
                        ; - MaxOpt::test1@11 (line 31)
                        ; - MaxOpt::runTests@3 (line 14)
  0x00000000029263e0: cmp    %r8d,%r11d
  0x00000000029263e3: jl     0x000000000292650c  ;*if_icmplt
                        ; - MaxOpt::test1@13 (line 31)
                        ; - MaxOpt::runTests@3 (line 14)
  0x00000000029263e9: mov    %r11d,%r8d
  0x00000000029263ec: inc    %r8d               ;*iinc
                        ; - MaxOpt::test1@22 (line 30)
                        ; - MaxOpt::runTests@3 (line 14)
  0x00000000029263ef: cmp    %r11d,%r8d
  0x00000000029263f2: jl     0x000000000292652d  ;*if_icmplt
                        ; - MaxOpt::test1@13 (line 31)
                        ; - MaxOpt::runTests@3 (line 14)
  0x00000000029263f8: mov    %r11d,%r9d
  0x00000000029263fb: add    $0x2,%r9d          ;*iinc
                        ; - MaxOpt::test1@22 (line 30)
                        ; - MaxOpt::runTests@3 (line 14)
  0x00000000029263ff: cmp    %r8d,%r9d
  0x0000000002926402: jl     0x000000000292650f  ;*if_icmplt
                        ; - MaxOpt::test1@13 (line 31)
                        ; - MaxOpt::runTests@3 (line 14)
  0x0000000002926408: mov    %r11d,%r8d
  0x000000000292640b: add    $0x3,%r8d          ;*iinc
                        ; - MaxOpt::test1@22 (line 30)
                        ; - MaxOpt::runTests@3 (line 14)
  0x000000000292640f: cmp    %r9d,%r8d
  0x0000000002926412: jl     0x0000000002926518  ;*if_icmplt
                        ; - MaxOpt::test1@13 (line 31)
                        ; - MaxOpt::runTests@3 (line 14)
  0x0000000002926418: mov    %r11d,%r9d
  0x000000000292641b: add    $0x4,%r9d          ;*iinc
                        ; - MaxOpt::test1@22 (line 30)
                        ; - MaxOpt::runTests@3 (line 14)
  0x000000000292641f: cmp    %r8d,%r9d
  0x0000000002926422: jl     0x000000000292650f  ;*if_icmplt
                        ; - MaxOpt::test1@13 (line 31)
                        ; - MaxOpt::runTests@3 (line 14)
  0x0000000002926428: mov    %r11d,%r8d
  0x000000000292642b: add    $0x5,%r8d          ;*iinc
                        ; - MaxOpt::test1@22 (line 30)
                        ; - MaxOpt::runTests@3 (line 14)
  0x000000000292642f: cmp    %r9d,%r8d
  0x0000000002926432: jl     0x0000000002926518  ;*if_icmplt
                        ; - MaxOpt::test1@13 (line 31)
                        ; - MaxOpt::runTests@3 (line 14)
  0x0000000002926438: mov    %r11d,%r9d
  0x000000000292643b: add    $0x6,%r9d          ;*iinc
                        ; - MaxOpt::test1@22 (line 30)
                        ; - MaxOpt::runTests@3 (line 14)
  0x000000000292643f: cmp    %r8d,%r9d
  0x0000000002926442: jl     0x000000000292650f  ;*if_icmplt
                        ; - MaxOpt::test1@13 (line 31)
                        ; - MaxOpt::runTests@3 (line 14)
  0x0000000002926448: mov    %r11d,%r8d
  0x000000000292644b: add    $0x7,%r8d          ;*iinc
                        ; - MaxOpt::test1@22 (line 30)
                        ; - MaxOpt::runTests@3 (line 14)
  0x000000000292644f: cmp    %r9d,%r8d
  0x0000000002926452: jl     0x0000000002926518  ;*if_icmplt
                        ; - MaxOpt::test1@13 (line 31)
                        ; - MaxOpt::runTests@3 (line 14)
  0x0000000002926458: mov    %r11d,%r9d
  0x000000000292645b: add    $0x8,%r9d          ;*iinc
                        ; - MaxOpt::test1@22 (line 30)
                        ; - MaxOpt::runTests@3 (line 14)
  0x000000000292645f: cmp    %r8d,%r9d
  0x0000000002926462: jl     0x000000000292650f  ;*if_icmplt
                        ; - MaxOpt::test1@13 (line 31)
                        ; - MaxOpt::runTests@3 (line 14)
  0x0000000002926468: mov    %r11d,%r8d
  0x000000000292646b: add    $0x9,%r8d          ;*iinc
                        ; - MaxOpt::test1@22 (line 30)
                        ; - MaxOpt::runTests@3 (line 14)
  0x000000000292646f: cmp    %r9d,%r8d
  0x0000000002926472: jl     0x0000000002926518  ;*if_icmplt
                        ; - MaxOpt::test1@13 (line 31)
                        ; - MaxOpt::runTests@3 (line 14)
  0x0000000002926478: mov    %r11d,%r9d
  0x000000000292647b: add    $0xa,%r9d          ;*iinc
                        ; - MaxOpt::test1@22 (line 30)
                        ; - MaxOpt::runTests@3 (line 14)
  0x000000000292647f: cmp    %r8d,%r9d
  0x0000000002926482: jl     0x000000000292650f  ;*if_icmplt
                        ; - MaxOpt::test1@13 (line 31)
                        ; - MaxOpt::runTests@3 (line 14)
  0x0000000002926488: mov    %r11d,%r8d
  0x000000000292648b: add    $0xb,%r8d          ;*iinc
                        ; - MaxOpt::test1@22 (line 30)
                        ; - MaxOpt::runTests@3 (line 14)
  0x000000000292648f: cmp    %r9d,%r8d
  0x0000000002926492: jl     0x0000000002926518  ;*if_icmplt
                        ; - MaxOpt::test1@13 (line 31)
                        ; - MaxOpt::runTests@3 (line 14)
  0x0000000002926498: mov    %r11d,%r9d
  0x000000000292649b: add    $0xc,%r9d          ;*iinc
                        ; - MaxOpt::test1@22 (line 30)
                        ; - MaxOpt::runTests@3 (line 14)
  0x000000000292649f: cmp    %r8d,%r9d
  0x00000000029264a2: jl     0x000000000292650f  ;*if_icmplt
                        ; - MaxOpt::test1@13 (line 31)
                        ; - MaxOpt::runTests@3 (line 14)
  0x00000000029264a4: mov    %r11d,%r8d
  0x00000000029264a7: add    $0xd,%r8d          ;*iinc
                        ; - MaxOpt::test1@22 (line 30)
                        ; - MaxOpt::runTests@3 (line 14)
  0x00000000029264ab: cmp    %r9d,%r8d
  0x00000000029264ae: jl     0x0000000002926518  ;*if_icmplt
                        ; - MaxOpt::test1@13 (line 31)
                        ; - MaxOpt::runTests@3 (line 14)
  0x00000000029264b0: mov    %r11d,%r9d
  0x00000000029264b3: add    $0xe,%r9d          ;*iinc
                        ; - MaxOpt::test1@22 (line 30)
                        ; - MaxOpt::runTests@3 (line 14)
  0x00000000029264b7: cmp    %r8d,%r9d
  0x00000000029264ba: jl     0x000000000292650f  ;*if_icmplt
                        ; - MaxOpt::test1@13 (line 31)
                        ; - MaxOpt::runTests@3 (line 14)
  0x00000000029264bc: mov    %r11d,%r8d
  0x00000000029264bf: add    $0xf,%r8d          ;*iinc
                        ; - MaxOpt::test1@22 (line 30)
                        ; - MaxOpt::runTests@3 (line 14)
  0x00000000029264c3: cmp    %r9d,%r8d
  0x00000000029264c6: jl     0x0000000002926518  ;*if_icmplt
                        ; - MaxOpt::test1@13 (line 31)
                        ; - MaxOpt::runTests@3 (line 14)
  0x00000000029264c8: add    $0x10,%r11d        ;*iinc
                        ; - MaxOpt::test1@22 (line 30)
                        ; - MaxOpt::runTests@3 (line 14)
  0x00000000029264cc: cmp    $0x2701,%r11d
  0x00000000029264d3: jl     0x00000000029263e0  ;*if_icmpge
                        ; - MaxOpt::test1@8 (line 30)
                        ; - MaxOpt::runTests@3 (line 14)
  0x00000000029264d9: cmp    $0x2710,%r11d
  0x00000000029264e0: jge    0x0000000002926500
  0x00000000029264e2: xchg   %ax,%ax            ;*iload_1
                        ; - MaxOpt::test1@11 (line 31)
                        ; - MaxOpt::runTests@3 (line 14)
  0x00000000029264e4: cmp    %r8d,%r11d
  0x00000000029264e7: jl     0x0000000002926532  ;*if_icmplt
                        ; - MaxOpt::test1@13 (line 31)
                        ; - MaxOpt::runTests@3 (line 14)
  0x00000000029264e9: mov    %r11d,%r10d
  0x00000000029264ec: inc    %r10d              ;*iinc
                        ; - MaxOpt::test1@22 (line 30)
                        ; - MaxOpt::runTests@3 (line 14)
  0x00000000029264ef: cmp    $0x2710,%r10d
  0x00000000029264f6: jge    0x0000000002926500  ;*if_icmpge
                        ; - MaxOpt::test1@8 (line 30)
                        ; - MaxOpt::runTests@3 (line 14)
  0x00000000029264f8: mov    %r11d,%r8d
  0x00000000029264fb: mov    %r10d,%r11d
  0x00000000029264fe: jmp    0x00000000029264e4
  0x0000000002926500: add    $0x20,%rsp
  0x0000000002926504: pop    %rbp
  0x0000000002926505: test   %eax,-0x26f650b(%rip)        # 0x0000000000230000
                        ;   {poll_return}
  0x000000000292650b: retq   
  0x000000000292650c: mov    %r11d,%r9d
  0x000000000292650f: mov    %r9d,%r11d
  0x0000000002926512: mov    %r8d,%r9d
  0x0000000002926515: mov    %r11d,%r8d
  0x0000000002926518: mov    $0xffffff65,%edx
  0x000000000292651d: mov    %r8d,0x4(%rsp)
  0x0000000002926522: mov    %r9d,0x8(%rsp)
  0x0000000002926527: callq  0x00000000028557a0  ; OopMap{off=364}
                        ;*if_icmplt
                        ; - MaxOpt::test1@13 (line 31)
                        ; - MaxOpt::runTests@3 (line 14)
                        ;   {runtime_call}
  0x000000000292652c: int3                      ;*if_icmplt
                        ; - MaxOpt::test1@13 (line 31)
                        ; - MaxOpt::runTests@3 (line 14)
  0x000000000292652d: mov    %r11d,%r9d
  0x0000000002926530: jmp    0x0000000002926518
  0x0000000002926532: mov    %r8d,%r9d
  0x0000000002926535: mov    %r11d,%r8d
  0x0000000002926538: jmp    0x0000000002926518
  0x000000000292653a: hlt    
  0x000000000292653b: hlt    
  0x000000000292653c: hlt    
  0x000000000292653d: hlt    
  0x000000000292653e: hlt    
  0x000000000292653f: hlt    
[Exception Handler]
 ...
I wonder why the method is not optimized. Maybe it's once more worth being asked as a separate question. But my gut feeling is that it is a side effect of the artificial test configuration, involving the final n and the usage of the loop variable for the inner expression. In similar (more realistic) setups, such useless, side-effect-free methods are usually eliminated rather reliably.