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0 Td (i\056e) Tj /R34 9.96260 Tf 9.68320 0 Td (\056) Tj /R50 9.96260 Tf -233.75900 -11.95510 Td [ (h) -0.19972 ] TJ /R46 9.96260 Tf 5.73984 0 Td [ (\050) -0.89997 ] TJ /R52 9.96260 Tf 3.87422 0 Td [ (x) -0.89997 ] TJ /R46 9.96260 Tf 6.04688 0 Td [ (\051) -432.88200 (\075) -0.79950 ] TJ /R64 9.96260 Tf 20.23590 7.47227 Td [ (P) -0.60039 ] TJ /R56 6.97380 Tf 10.51720 -2.46328 Td [ (n) -0.19955 ] TJ 7.99766 TL T* [ (i) -0.20042 ] TJ /R40 6.97380 Tf 2.81797 0 Td [ (\0751) -0.49887 ] TJ /R50 9.96260 Tf 12.24570 2.98867 Td [ (h) -0.20095 ] TJ /R46 9.96260 Tf 5.74023 0 Td [ (\050) -0.89936 ] TJ /R52 9.96260 Tf 3.87383 0 Td [ (x) -0.89936 ] TJ /R56 6.97380 Tf 6.04727 -1.49375 Td [ (i) -0.19955 ] TJ /R46 9.96260 Tf 3.31680 1.49375 Td [ (\051) -0.89936 ] TJ /R34 9.96260 Tf 3.87422 0 Td [ (\051) -333.00700 (b) 20.00160 (ut) -334.01000 (not) -332.98600 (necessarily) -334.00600 (con) 39.99820 (v) 14.98280 (e) 15.01220 (x\056) -560.01700 (T) 79.99160 (ypical) ] TJ -84.33010 -11.95470 Td [ (e) 15.01280 (xamples) -363.99100 (of) ] TJ /R50 9.96260 Tf 53.03280 0 Td [ (h) -0.20095 ] TJ /R46 9.96260 Tf 5.74023 0 Td [ (\050) -0.89936 ] TJ /R52 9.96260 Tf 3.87500 0 Td [ (x) -0.89936 ] TJ /R46 9.96260 Tf 6.04570 0 Td [ (\051) -0.89936 ] TJ /R34 9.96260 Tf 7.50234 0 Td [ (include) -363.99700 (the) -364.01000 (bound) -363.99300 (constrained) -363.99300 (function) ] TJ -76.19610 -11.95510 Td [ (and) -249.99200 (the) ] TJ /R50 9.96260 Tf 31.54100 0 Td [ (\140) -0.70025 ] TJ /R40 6.97380 Tf 4.15078 -1.49492 Td [ (0) -0.49974 ] TJ /R34 9.96260 Tf 6.96016 1.49492 Td (and) Tj /R50 9.96260 Tf 16.87700 0 Td [ (\140) -0.69964 ] TJ /R40 6.97380 Tf 4.15117 -1.49492 Td [ (1) -0.50062 ] TJ /R34 9.96260 Tf 6.95977 1.49492 Td [ (norm) -250.01800 (functions\056) ] TJ -58.68480 -11.95630 Td [ (The) -404.98700 (optimi) 0.98513 (zation) -405.01500 (in) -405.01800 (\050) ] TJ ET Q 1 0 0 rg q 10 0 0 10 0 0 cm BT /R34 9.96260 Tf 1 0 0 1 151.09300 116.86500 Tm (1) Tj ET Q 0 g q 10 0 0 10 0 0 cm BT /R34 9.96260 Tf 1 0 0 1 156.07500 116.86500 Tm [ (\051) -404.01500 (is) -405.01700 <0365> 14.98770 (xible) -403.99100 (enough) -405.01100 (to) -403.99900 (model) -405.00600 (a) ] TJ -105.96300 -11.95470 Td [ (v) 24.98110 (ariety) -342.99400 (of) -342.02000 (applications) -343 (of) -342.02000 (interest) -342.98100 (in) -342.98900 (both) -342 (computer) -343.01900 (vision) ] TJ 11.95510 TL T* [ (and) -362.01300 (machine) -362.98200 (learning\054) -389.99400 (including) -362.01600 (compressi) 25.00560 (v) 14.98280 (e) -361.98400 (sensing) -363.00800 (\133) ] TJ ET Q 0 0.58789 0 rg q 10 0 0 10 0 0 cm BT /R34 9.96260 Tf 1 0 0 1 275.57600 92.95510 Tm (7) Tj ET Q 0 g q 10 0 0 10 0 0 cm BT /R34 9.96260 Tf 1 0 0 1 280.55700 92.95510 Tm (\135\054) Tj -230.44500 -11.95510 Td [ (nonne) 14.99380 (g) 4.98446 (ati) 24.98600 (v) 14.98280 (e) -297.01400 (matrix) -298.00400 (f) 9.99466 (actorization) -296.98600 (\133) ] TJ ET Q 0 0.58789 0 rg q 10 0 0 10 0 0 cm BT /R34 9.96260 Tf 1 0 0 1 186.68000 81 Tm (16) Tj ET Q 0 g q 10 0 0 10 0 0 cm BT /R34 9.96260 Tf 1 0 0 1 196.64300 81 Tm (\054) Tj ET Q 0 0.58789 0 rg q 10 0 0 10 0 0 cm BT /R34 9.96260 Tf 1 0 0 1 202.10200 81 Tm (18) Tj ET Q 0 g q 10 0 0 10 0 0 cm BT /R34 9.96260 Tf 1 0 0 1 212.06400 81 Tm (\054) Tj ET Q 0 0.58789 0 rg q 10 0 0 10 0 0 cm BT /R34 9.96260 Tf 1 0 0 1 217.51400 81 Tm (9) Tj ET Q 0 g q 10 0 0 10 0 0 cm BT /R34 9.96260 Tf 1 0 0 1 222.49500 81 Tm [ (\135\054) -309.00700 (sparse) -297.98500 (coding) ] TJ 86.36680 459.37200 Td (\133) Tj ET Q 0 0.58789 0 rg q 10 0 0 10 0 0 cm BT /R34 9.96260 Tf 1 0 0 1 312.18000 540.37200 Tm (17) Tj ET Q 0 g q 10 0 0 10 0 0 cm BT /R34 9.96260 Tf 1 0 0 1 322.14200 540.37200 Tm (\054) Tj ET Q 0 0.58789 0 rg q 10 0 0 10 0 0 cm BT /R34 9.96260 Tf 1 0 0 1 327.44200 540.37200 Tm (1) Tj ET Q 0 g q 10 0 0 10 0 0 cm BT /R34 9.96260 Tf 1 0 0 1 332.42300 540.37200 Tm (\054) Tj ET Q 0 0.58789 0 rg q 10 0 0 10 0 0 cm BT /R34 9.96260 Tf 1 0 0 1 337.72300 540.37200 Tm (2) Tj ET Q 0 g q 10 0 0 10 0 0 cm BT /R34 9.96260 Tf 1 0 0 1 342.70500 540.37200 Tm (\054) Tj ET Q 0 0.58789 0 rg q 10 0 0 10 0 0 cm BT /R34 9.96260 Tf 1 0 0 1 348.00500 540.37200 Tm (29) Tj ET Q 0 g q 10 0 0 10 0 0 cm BT /R34 9.96260 Tf 1 0 0 1 357.96700 540.37200 Tm [ (\135\054) -289.99100 (support) -282.00200 (v) 14.98280 (ector) -281.99200 (machine) -282.01700 (\133) ] TJ ET Q 0 0.58789 0 rg q 10 0 0 10 0 0 cm BT /R34 9.96260 Tf 1 0 0 1 466.79900 540.37200 Tm (11) Tj ET Q 0 g q 10 0 0 10 0 0 cm BT /R34 9.96260 Tf 1 0 0 1 476.76100 540.37200 Tm [ (\135\054) -289.99100 (logistic) -281.99200 (re) 15.00730 (gres\055) ] TJ -167.89900 -11.95470 Td [ (sion) -252.01400 (\133) ] TJ ET Q 0 0.58789 0 rg q 10 0 0 10 0 0 cm BT /R34 9.96260 Tf 1 0 0 1 331.29800 528.41700 Tm (38) Tj ET Q 0 g q 10 0 0 10 0 0 cm BT /R34 9.96260 Tf 1 0 0 1 341.26100 528.41700 Tm [ (\135\054) -253.01700 (subspace) -251.98200 (clustering) -252.00700 (\133) ] TJ ET Q 0 0.58789 0 rg q 10 0 0 10 0 0 cm BT /R34 9.96260 Tf 1 0 0 1 433.18600 528.41700 Tm (8) Tj ET Q 0 g q 10 0 0 10 0 0 cm BT /R34 9.96260 Tf 1 0 0 1 438.16700 528.41700 Tm [ (\135\054) -253.01700 (to) -251.98700 (name) -253.00700 (a) -252.00200 (fe) 25.00560 (w) 65.01370 (\056) -317.00100 (Although) ] TJ -129.30500 -11.95510 Td [ (we) -353.00200 (only) -353.99700 (focus) -352.99300 (on) -354.01000 (the) -352.99300 (quadratic) -354.00500 (function) ] TJ /R50 9.96260 Tf 167.97000 0 Td [ (q) -0.40189 ] TJ /R46 9.96260 Tf 4.80508 0 Td [ (\050) -0.90181 ] TJ /R58 9.96260 Tf 3.87383 0 Td [ <01> -0.80379 ] TJ /R46 9.96260 Tf 2.76797 0 Td [ (\051) -0.90181 ] TJ /R34 9.96260 Tf 3.87422 0 Td [ (\054) -378.99100 (our) -354.01400 (method) ] TJ -183.29100 -11.95510 Td [ (can) -341.98500 (be) -341.00200 (e) 15.01220 (xtended) -342.00200 (to) -342.00900 (handle) -342.00700 (general) -341.00200 (composite) -341.98200 (functions) -341.98700 (as) ] TJ 11.95510 TL T* [ (well\054) -237.98500 (by) -233.99000 (considering) -234.98500 (a) -234.98500 (typical) -234.99500 (Ne) 25.01540 (wton) -234.02000 (approximation) -235.00500 (of) -235.02000 (the) ] TJ 11.95590 TL T* [ (objecti) 24.99830 (v) 14.98280 (e) -250.00200 (\133) ] TJ ET Q 0 0.58789 0 rg q 10 0 0 10 0 0 cm BT /R34 9.96260 Tf 1 0 0 1 350.79500 480.59600 Tm (35) Tj ET Q 0 g q 10 0 0 10 0 0 cm BT /R34 9.96260 Tf 1 0 0 1 360.75700 480.59600 Tm (\054) Tj ET Q 0 0.58789 0 rg q 10 0 0 10 0 0 cm BT /R34 9.96260 Tf 1 0 0 1 365.73900 480.59600 Tm (40) Tj ET Q 0 g q 10 0 0 10 0 0 cm BT /R34 9.96260 Tf 1 0 0 1 375.70100 480.59600 Tm (\135\056) Tj -54.88400 -13.14300 Td [ (The) -297.98500 (most) -298 (popular) -298.00900 (method) -298 (for) -297.99000 (solving) -297.99000 (\050) ] TJ ET Q 1 0 0 rg q 10 0 0 10 0 0 cm BT /R34 9.96260 Tf 1 0 0 1 478.09600 467.45300 Tm (1) Tj ET Q 0 g q 10 0 0 10 0 0 cm BT /R34 9.96260 Tf 1 0 0 1 483.07800 467.45300 Tm [ (\051) -299.01400 (is) -298.01400 (perhaps) -298.01900 (the) ] TJ -174.21600 -11.95510 Td [ (proximal) -444.98900 (gradient) -445.00700 (method) -444.99400 (\133) ] TJ ET Q 0 0.58789 0 rg q 10 0 0 10 0 0 cm BT /R34 9.96260 Tf 1 0 0 1 423.99000 455.49800 Tm (25) Tj ET Q 0 g q 10 0 0 10 0 0 cm BT /R34 9.96260 Tf 1 0 0 1 433.95200 455.49800 Tm (\054) Tj ET Q 0 0.58789 0 rg q 10 0 0 10 0 0 cm BT /R34 9.96260 Tf 1 0 0 1 440.87700 455.49800 Tm (3) Tj ET Q 0 g q 10 0 0 10 0 0 cm BT /R34 9.96260 Tf 1 0 0 1 445.85800 455.49800 Tm [ (\135\056) -894.98800 (It) -444.98000 (considers) -445 (a) -444.98900 <0278> 14.99750 (ed\055) ] TJ -136.99600 -11.95590 Td [ (point) -375.98600 (proximal) -375.98100 (iterati) 24.99340 (v) 14.98280 (e) -375.98100 (procedure) ] TJ /R52 9.96260 Tf 143.52400 0 Td [ (x) -0.89691 ] TJ /R56 6.97380 Tf 6.04727 3.61602 Td [ (k) -0.30107 ] TJ /R40 6.97380 Tf 4.40391 0 Td [ (\0531) -0.49712 ] TJ /R46 9.96260 Tf 15.67890 -3.61602 Td [ (\075) -0.80379 ] TJ /R34 9.96260 Tf 12.84180 0 Td (prox) Tj /R56 6.97380 Tf 18.26210 -2.65508 Td [ <0d> -61.12440 (h) -0.79819 ] TJ /R46 9.96260 Tf 9.77617 2.65508 Td [ (\050) -0.90181 ] TJ /R52 9.96260 Tf 3.87383 0 Td [ (x) -0.89691 ] TJ /R56 6.97380 Tf 6.04688 3.61602 Td [ (k) -0.30107 ] TJ /R58 9.96260 Tf 8.04609 -3.61602 Td [ <00> -0.80379 ] TJ /R50 9.96260 Tf -228.50100 -13.46520 Td [ <0d> -0.70086 ] TJ /R54 9.96260 Tf 5.71094 0 Td [ (O) -0.20095 ] TJ /R50 9.96260 Tf 7.19492 0 Td [ (q) -0.40189 ] TJ /R46 9.96260 Tf 4.80508 0 Td [ (\050) -0.90181 ] TJ /R52 9.96260 Tf 3.87500 0 Td [ (x) -0.90181 ] TJ /R56 6.97380 Tf 6.04609 3.61523 Td [ (k) -0.29757 ] TJ /R46 9.96260 Tf 4.90195 -3.61523 Td [ (\051) -0.90181 (\051) -0.89936 ] TJ /R34 9.96260 Tf 10.74380 0 Td [ (based) -301.00100 (on) -300.01900 (the) -301.00100 (current) -299.98900 (gradient) ] TJ /R54 9.96260 Tf 120.65700 0 Td [ (O) -0.19605 ] TJ /R50 9.96260 Tf 7.19492 0 Td [ (q) -0.40189 ] TJ /R46 9.96260 Tf 4.80508 0 Td [ (\050) -0.90181 ] TJ /R52 9.96260 Tf 3.87422 0 Td [ (x) -0.89691 ] TJ /R56 6.97380 Tf 6.04688 3.61523 Td [ (k) -0.30107 ] TJ /R46 9.96260 Tf 4.90195 -3.61523 Td [ (\051) -0.90181 ] TJ /R34 9.96260 Tf 3.87422 0 Td [ (\056) -461.99600 (Here) -299.99900 (the) ] TJ -194.63200 -11.95510 Td [ (proximal) -216.98800 (operator) -215.99600 (prox) ] TJ /R40 6.97380 Tf 91.88200 -1.25977 Td [ (\176) -0.50062 ] TJ /R56 6.97380 Tf -0.13203 -1.84023 Td [ (h) -0.80169 ] TJ /R46 9.96260 Tf 5.16172 3.10000 Td [ (\050) -0.90181 ] TJ /R52 9.96260 Tf 3.87422 0 Td (a) Tj /R46 9.96260 Tf 5.56992 0 Td [ (\051) -278.90900 (\075) -277.80700 (a) -1.01454 (r) 0.27936 (g) -180.98400 (m) -0.30387 (i) -0.79889 (n) -0.60284 ] TJ /R48 6.97380 Tf 49.42500 -1.49492 Td [ (x) -0.70017 ] TJ /R40 6.97380 Tf 10.27500 5.41719 Td [ (1) -0.49712 ] TJ ET Q 4749.18000 4206.12000 m 4788.89000 4206.12000 l S q 10 0 0 10 0 0 cm BT /R40 6.97380 Tf 1 0 0 1 474.91800 414.68600 Tm [ (2) -0.49712 ] TJ /R58 9.96260 Tf 5.16719 3.43594 Td (k) Tj /R52 9.96260 Tf 4.98086 0 Td [ (x) -0.89691 ] TJ /R58 9.96260 Tf 7.03281 0 Td [ <00> -0.80379 ] TJ /R52 9.96260 Tf 8.73633 0 Td (a) Tj /R58 9.96260 Tf 5.56875 0 Td (k) Tj /R40 6.97380 Tf 4.98125 3.61523 Td [ (2) -0.49712 ] TJ 6.08828 TL T* [ (2) -0.49712 ] TJ /R46 9.96260 Tf 5.45586 2.47305 Td [ (\053) -0.80379 ] TJ 8.83789 2.62930 Td (\176) Tj /R50 9.96260 Tf -0.10312 -2.62930 Td [ (h) -0.19605 ] TJ /R46 9.96260 Tf 5.74023 0 Td [ (\050) -0.90181 ] TJ /R52 9.96260 Tf 3.87500 0 Td [ (x) -0.89691 ] TJ /R46 9.96260 Tf 6.04688 0 Td [ (\051) -0.90181 ] TJ /R34 9.96260 Tf -232.37600 -11.95470 Td [ (can) -384.01700 (often) -384.98500 (be) -384.01400 (e) 25.01050 (v) 24.98110 (aluated) -384.98200 (analytically) 65.00390 (\054) ] TJ /R50 9.96260 Tf 149.19500 0 Td [ <0d> -0.69596 ] TJ /R46 9.96260 Tf 10.95900 0 Td [ (\075) -527.80400 (1) ] TJ /R50 9.96260 Tf 17.97700 0 Td [ (\075L) -0.60284 ] TJ /R34 9.96260 Tf 15.59100 0 Td [ (is) -384 (the) -384.98500 (step) ] TJ -193.72200 -11.95630 Td [ (size) -356.01400 (with) ] TJ /R50 9.96260 Tf 40.29690 0 Td [ (L) -0.60039 ] TJ /R34 9.96260 Tf 10.32580 0 Td [ (being) -356.00200 (the) -356.01200 (local) -356.00900 (\050or) -355.98000 (global\051) -356 (Lipschit) 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/R58 9.96260 Tf T* [ (O) -0.10047 ] TJ /R46 9.96260 Tf 8.20781 0 Td [ (\050) -0.90181 ] TJ /R50 9.96260 Tf 3.87422 0 Td [ (L) -0.60039 (\075k) -0.60039 ] TJ /R40 6.97380 Tf 17.26170 3.61523 Td [ (2) -0.50062 ] TJ /R46 9.96260 Tf 4.46992 -3.61523 Td [ (\051) -0.90181 ] TJ /R34 9.96260 Tf 3.87422 0 Td [ (\056) -372.01400 (T) 35.01870 (ighter) -270.99600 (estimates) -270 (of) -271.01400 (the) -271.00400 (local) -269.98400 (Lipschitz) -270.97900 (constant) ] TJ -37.68790 -11.95510 Td [ (leads) -344.99100 (to) -344.98900 (better) -344.99400 (con) 39.99820 (v) 14.98280 (er) 17.98960 (gence) -345.00600 (rate\054) -368.99700 (b) 20.00160 (ut) -344.99100 (it) -344.98700 <7363617269026573> -344.98200 (additional) ] TJ 11.95590 TL T* [ (computation) -281.00200 (o) 14.98280 (v) 14.98280 (erhead) -281.01900 (to) -280.01900 (compute) ] TJ /R50 9.96260 Tf 139.28000 0 Td [ (L) -0.60284 ] TJ /R34 9.96260 Tf 6.78008 0 Td [ (\056) -402.98700 (Our) -279.98800 (method) -280.98300 (is) -280.99700 (also) 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