Convex optimization

Convex optimization is a subfield of mathematical optimization that studies the problem of minimizing convex functions over convex sets (or, equivalently, maximizing concave functions over convex sets). Many classes of convex optimization problems admit polynomial-time algorithms,^[1] whereas mathematical optimization is in general NP-hard.^[2]^[3]^[4]

^ Nesterov & Nemirovskii 1994
^ Murty, Katta; Kabadi, Santosh (1987). "Some NP-complete problems in quadratic and nonlinear programming". Mathematical Programming. 39 (2): 117–129. doi:10.1007/BF02592948. hdl:2027.42/6740. S2CID 30500771.
^ Sahni, S. "Computationally related problems," in SIAM Journal on Computing, 3, 262--279, 1974.
^ Pardalos, Panos M.; Vavasis, Stephen A. (1991). "Quadratic programming with one negative eigenvalue is NP-hard". Journal of Global Optimization. 1: 15–22. doi:10.1007/BF00120662.

[Nesterov_1994-1] Nesterov & Nemirovskii 1994

[2] Murty, Katta; Kabadi, Santosh (1987). "Some NP-complete problems in quadratic and nonlinear programming". Mathematical Programming. 39 (2): 117–129. doi:10.1007/BF02592948. hdl:2027.42/6740. S2CID 30500771.

[3] Sahni, S. "Computationally related problems," in SIAM Journal on Computing, 3, 262--279, 1974.

[4] Pardalos, Panos M.; Vavasis, Stephen A. (1991). "Quadratic programming with one negative eigenvalue is NP-hard". Journal of Global Optimization. 1: 15–22. doi:10.1007/BF00120662.

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