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Lower convex envelope

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252: 224: 50: 124: 73: 108: 293: 317: 286: 279: 312: 76: 53: 259: 26: 219:{\displaystyle {\breve {f}}(x)=\sup\{g(x)\mid g{\text{ is convex and }}g\leq f{\text{ over }}\}.} 115: 263: 240: 58: 81: 306: 235: 17: 251: 111: 267: 127: 84: 61: 29: 218: 102: 67: 44: 152: 110:is defined at each point of the interval as the 287: 8: 210: 155: 294: 280: 190: 176: 129: 128: 126: 83: 60: 31: 30: 28: 7: 248: 246: 118:that lie under that function, i.e. 14: 250: 207: 195: 167: 161: 146: 140: 97: 85: 1: 266:. You can help Knowledge by 45:{\displaystyle {\breve {f}}} 318:Mathematical analysis stubs 334: 245: 178: is convex and  262:–related article is a 220: 104: 69: 46: 260:mathematical analysis 221: 105: 70: 47: 22:lower convex envelope 125: 82: 59: 27: 216: 100: 65: 42: 275: 274: 193: 179: 137: 68:{\displaystyle f} 39: 325: 296: 289: 282: 254: 247: 225: 223: 222: 217: 194: 192: over  191: 180: 177: 139: 138: 130: 116:convex functions 109: 107: 106: 103:{\displaystyle } 101: 74: 72: 71: 66: 51: 49: 48: 43: 41: 40: 32: 333: 332: 328: 327: 326: 324: 323: 322: 313:Convex analysis 303: 302: 301: 300: 232: 123: 122: 80: 79: 57: 56: 25: 24: 12: 11: 5: 331: 329: 321: 320: 315: 305: 304: 299: 298: 291: 284: 276: 273: 272: 255: 244: 243: 241:Lower envelope 238: 231: 228: 227: 226: 215: 212: 209: 206: 203: 200: 197: 189: 186: 183: 175: 172: 169: 166: 163: 160: 157: 154: 151: 148: 145: 142: 136: 133: 99: 96: 93: 90: 87: 75:defined on an 64: 38: 35: 13: 10: 9: 6: 4: 3: 2: 330: 319: 316: 314: 311: 310: 308: 297: 292: 290: 285: 283: 278: 277: 271: 269: 265: 261: 256: 253: 249: 242: 239: 237: 234: 233: 229: 213: 204: 201: 198: 187: 184: 181: 173: 170: 164: 158: 149: 143: 134: 131: 121: 120: 119: 117: 113: 94: 91: 88: 78: 62: 55: 36: 33: 23: 19: 268:expanding it 257: 21: 15: 236:Convex hull 18:mathematics 307:Categories 185:≤ 171:∣ 135:˘ 37:˘ 230:See also 112:supremum 77:interval 54:function 114:of all 20:, the 258:This 52:of a 264:stub 153:sup 16:In 309:: 295:e 288:t 281:v 270:. 214:. 211:} 208:] 205:b 202:, 199:a 196:[ 188:f 182:g 174:g 168:) 165:x 162:( 159:g 156:{ 150:= 147:) 144:x 141:( 132:f 98:] 95:b 92:, 89:a 86:[ 63:f 34:f

Index

mathematics
function
interval
supremum
convex functions
Convex hull
Lower envelope
Stub icon
mathematical analysis
stub
expanding it
v
t
e
Categories
Convex analysis
Mathematical analysis stubs

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