### A Pluto.jl notebook ###
# v0.15.1

using Markdown
using InteractiveUtils

# ╔═╡ 457e4d2c-0225-11ec-1b21-7b47b5339342
using JuMP, Ipopt

# ╔═╡ 7f3a1eb1-63a7-4062-9dd6-e88e31e961da
model = Model(Ipopt.Optimizer)

# ╔═╡ af9691bd-e434-48e5-bb53-7b63b0d152a9
begin
  @variable(model, x)
  @variable(model, y)
end

# ╔═╡ c199a311-3874-4f2c-a6e9-270cbc40cedd
@NLobjective(model, Min, (1 - x)^2 + 100 * (y - x^2)^2)

# ╔═╡ 8b62d21e-9774-4c5c-9667-c6379e78733c
optimize!(model)

# ╔═╡ 5963c706-4143-443f-aaf0-d61001bfce04
value(x)

# ╔═╡ 2a365ed7-5e15-4b96-851f-2fa556941b51
value(y)

# ╔═╡ 00000000-0000-0000-0000-000000000001
PLUTO_PROJECT_TOML_CONTENTS = """
[deps]
Ipopt = "b6b21f68-93f8-5de0-b562-5493be1d77c9"
JuMP = "4076af6c-e467-56ae-b986-b466b2749572"

[compat]
Ipopt = "~0.7.0"
JuMP = "~0.21.9"
"""

# ╔═╡ 00000000-0000-0000-0000-000000000002
PLUTO_MANIFEST_TOML_CONTENTS = """
# This file is machine-generated - editing it directly is not advised

[[ASL_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "370cafc70604b2522f2c7cf9915ebcd17b4cd38b"
uuid = "ae81ac8f-d209-56e5-92de-9978fef736f9"
version = "0.1.2+0"

[[ArgTools]]
uuid = "0dad84c5-d112-42e6-8d28-ef12dabb789f"

[[Artifacts]]
uuid = "56f22d72-fd6d-98f1-02f0-08ddc0907c33"

[[Base64]]
uuid = "2a0f44e3-6c83-55bd-87e4-b1978d98bd5f"

[[BenchmarkTools]]
deps = ["JSON", "Logging", "Printf", "Statistics", "UUIDs"]
git-tree-sha1 = "aa3aba5ed8f882ed01b71e09ca2ba0f77f44a99e"
uuid = "6e4b80f9-dd63-53aa-95a3-0cdb28fa8baf"
version = "1.1.3"

[[BinaryProvider]]
deps = ["Libdl", "Logging", "SHA"]
git-tree-sha1 = "ecdec412a9abc8db54c0efc5548c64dfce072058"
uuid = "b99e7846-7c00-51b0-8f62-c81ae34c0232"
version = "0.5.10"

[[Bzip2_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "19a35467a82e236ff51bc17a3a44b69ef35185a2"
uuid = "6e34b625-4abd-537c-b88f-471c36dfa7a0"
version = "1.0.8+0"

[[Calculus]]
deps = ["LinearAlgebra"]
git-tree-sha1 = "f641eb0a4f00c343bbc32346e1217b86f3ce9dad"
uuid = "49dc2e85-a5d0-5ad3-a950-438e2897f1b9"
version = "0.5.1"

[[ChainRulesCore]]
deps = ["Compat", "LinearAlgebra", "SparseArrays"]
git-tree-sha1 = "bdc0937269321858ab2a4f288486cb258b9a0af7"
uuid = "d360d2e6-b24c-11e9-a2a3-2a2ae2dbcce4"
version = "1.3.0"

[[CodecBzip2]]
deps = ["Bzip2_jll", "Libdl", "TranscodingStreams"]
git-tree-sha1 = "2e62a725210ce3c3c2e1a3080190e7ca491f18d7"
uuid = "523fee87-0ab8-5b00-afb7-3ecf72e48cfd"
version = "0.7.2"

[[CodecZlib]]
deps = ["TranscodingStreams", "Zlib_jll"]
git-tree-sha1 = "ded953804d019afa9a3f98981d99b33e3db7b6da"
uuid = "944b1d66-785c-5afd-91f1-9de20f533193"
version = "0.7.0"

[[CommonSubexpressions]]
deps = ["MacroTools", "Test"]
git-tree-sha1 = "7b8a93dba8af7e3b42fecabf646260105ac373f7"
uuid = "bbf7d656-a473-5ed7-a52c-81e309532950"
version = "0.3.0"

[[Compat]]
deps = ["Base64", "Dates", "DelimitedFiles", "Distributed", "InteractiveUtils", "LibGit2", "Libdl", "LinearAlgebra", "Markdown", "Mmap", "Pkg", "Printf", "REPL", "Random", "SHA", "Serialization", "SharedArrays", "Sockets", "SparseArrays", "Statistics", "Test", "UUIDs", "Unicode"]
git-tree-sha1 = "727e463cfebd0c7b999bbf3e9e7e16f254b94193"
uuid = "34da2185-b29b-5c13-b0c7-acf172513d20"
version = "3.34.0"

[[CompilerSupportLibraries_jll]]
deps = ["Artifacts", "Libdl"]
uuid = "e66e0078-7015-5450-92f7-15fbd957f2ae"

[[DataStructures]]
deps = ["Compat", "InteractiveUtils", "OrderedCollections"]
git-tree-sha1 = "7d9d316f04214f7efdbb6398d545446e246eff02"
uuid = "864edb3b-99cc-5e75-8d2d-829cb0a9cfe8"
version = "0.18.10"

[[Dates]]
deps = ["Printf"]
uuid = "ade2ca70-3891-5945-98fb-dc099432e06a"

[[DelimitedFiles]]
deps = ["Mmap"]
uuid = "8bb1440f-4735-579b-a4ab-409b98df4dab"

[[DiffResults]]
deps = ["StaticArrays"]
git-tree-sha1 = "c18e98cba888c6c25d1c3b048e4b3380ca956805"
uuid = "163ba53b-c6d8-5494-b064-1a9d43ac40c5"
version = "1.0.3"

[[DiffRules]]
deps = ["NaNMath", "Random", "SpecialFunctions"]
git-tree-sha1 = "3ed8fa7178a10d1cd0f1ca524f249ba6937490c0"
uuid = "b552c78f-8df3-52c6-915a-8e097449b14b"
version = "1.3.0"

[[Distributed]]
deps = ["Random", "Serialization", "Sockets"]
uuid = "8ba89e20-285c-5b6f-9357-94700520ee1b"

[[DocStringExtensions]]
deps = ["LibGit2"]
git-tree-sha1 = "a32185f5428d3986f47c2ab78b1f216d5e6cc96f"
uuid = "ffbed154-4ef7-542d-bbb7-c09d3a79fcae"
version = "0.8.5"

[[Downloads]]
deps = ["ArgTools", "LibCURL", "NetworkOptions"]
uuid = "f43a241f-c20a-4ad4-852c-f6b1247861c6"

[[ForwardDiff]]
deps = ["CommonSubexpressions", "DiffResults", "DiffRules", "LinearAlgebra", "NaNMath", "Printf", "Random", "SpecialFunctions", "StaticArrays"]
git-tree-sha1 = "b5e930ac60b613ef3406da6d4f42c35d8dc51419"
uuid = "f6369f11-7733-5829-9624-2563aa707210"
version = "0.10.19"

[[HTTP]]
deps = ["Base64", "Dates", "IniFile", "Logging", "MbedTLS", "NetworkOptions", "Sockets", "URIs"]
git-tree-sha1 = "44e3b40da000eab4ccb1aecdc4801c040026aeb5"
uuid = "cd3eb016-35fb-5094-929b-558a96fad6f3"
version = "0.9.13"

[[IniFile]]
deps = ["Test"]
git-tree-sha1 = "098e4d2c533924c921f9f9847274f2ad89e018b8"
uuid = "83e8ac13-25f8-5344-8a64-a9f2b223428f"
version = "0.5.0"

[[InteractiveUtils]]
deps = ["Markdown"]
uuid = "b77e0a4c-d291-57a0-90e8-8db25a27a240"

[[Ipopt]]
deps = ["BinaryProvider", "Ipopt_jll", "Libdl", "LinearAlgebra", "MathOptInterface", "MathProgBase"]
git-tree-sha1 = "380786b4929b8d18d76e909c6b2eca355b7c3bd6"
uuid = "b6b21f68-93f8-5de0-b562-5493be1d77c9"
version = "0.7.0"

[[Ipopt_jll]]
deps = ["ASL_jll", "Artifacts", "CompilerSupportLibraries_jll", "JLLWrappers", "Libdl", "MUMPS_seq_jll", "OpenBLAS32_jll", "Pkg"]
git-tree-sha1 = "82124f27743f2802c23fcb05febc517d0b15d86e"
uuid = "9cc047cb-c261-5740-88fc-0cf96f7bdcc7"
version = "3.13.4+2"

[[IrrationalConstants]]
git-tree-sha1 = "f76424439413893a832026ca355fe273e93bce94"
uuid = "92d709cd-6900-40b7-9082-c6be49f344b6"
version = "0.1.0"

[[JLLWrappers]]
deps = ["Preferences"]
git-tree-sha1 = "642a199af8b68253517b80bd3bfd17eb4e84df6e"
uuid = "692b3bcd-3c85-4b1f-b108-f13ce0eb3210"
version = "1.3.0"

[[JSON]]
deps = ["Dates", "Mmap", "Parsers", "Unicode"]
git-tree-sha1 = "8076680b162ada2a031f707ac7b4953e30667a37"
uuid = "682c06a0-de6a-54ab-a142-c8b1cf79cde6"
version = "0.21.2"

[[JSONSchema]]
deps = ["HTTP", "JSON", "ZipFile"]
git-tree-sha1 = "b84ab8139afde82c7c65ba2b792fe12e01dd7307"
uuid = "7d188eb4-7ad8-530c-ae41-71a32a6d4692"
version = "0.3.3"

[[JuMP]]
deps = ["Calculus", "DataStructures", "ForwardDiff", "JSON", "LinearAlgebra", "MathOptInterface", "MutableArithmetics", "NaNMath", "Printf", "Random", "SparseArrays", "SpecialFunctions", "Statistics"]
git-tree-sha1 = "4f0a771949bbe24bf70c89e8032c107ebe03f6ba"
uuid = "4076af6c-e467-56ae-b986-b466b2749572"
version = "0.21.9"

[[LibCURL]]
deps = ["LibCURL_jll", "MozillaCACerts_jll"]
uuid = "b27032c2-a3e7-50c8-80cd-2d36dbcbfd21"

[[LibCURL_jll]]
deps = ["Artifacts", "LibSSH2_jll", "Libdl", "MbedTLS_jll", "Zlib_jll", "nghttp2_jll"]
uuid = "deac9b47-8bc7-5906-a0fe-35ac56dc84c0"

[[LibGit2]]
deps = ["Base64", "NetworkOptions", "Printf", "SHA"]
uuid = "76f85450-5226-5b5a-8eaa-529ad045b433"

[[LibSSH2_jll]]
deps = ["Artifacts", "Libdl", "MbedTLS_jll"]
uuid = "29816b5a-b9ab-546f-933c-edad1886dfa8"

[[Libdl]]
uuid = "8f399da3-3557-5675-b5ff-fb832c97cbdb"

[[LinearAlgebra]]
deps = ["Libdl"]
uuid = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e"

[[LogExpFunctions]]
deps = ["DocStringExtensions", "IrrationalConstants", "LinearAlgebra"]
git-tree-sha1 = "3d682c07e6dd250ed082f883dc88aee7996bf2cc"
uuid = "2ab3a3ac-af41-5b50-aa03-7779005ae688"
version = "0.3.0"

[[Logging]]
uuid = "56ddb016-857b-54e1-b83d-db4d58db5568"

[[METIS_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "2dc1a9fc87e57e32b1fc186db78811157b30c118"
uuid = "d00139f3-1899-568f-a2f0-47f597d42d70"
version = "5.1.0+5"

[[MUMPS_seq_jll]]
deps = ["Artifacts", "CompilerSupportLibraries_jll", "JLLWrappers", "Libdl", "METIS_jll", "OpenBLAS32_jll", "Pkg"]
git-tree-sha1 = "1a11a84b2af5feb5a62a820574804056cdc59c39"
uuid = "d7ed1dd3-d0ae-5e8e-bfb4-87a502085b8d"
version = "5.2.1+4"

[[MacroTools]]
deps = ["Markdown", "Random"]
git-tree-sha1 = "0fb723cd8c45858c22169b2e42269e53271a6df7"
uuid = "1914dd2f-81c6-5fcd-8719-6d5c9610ff09"
version = "0.5.7"

[[Markdown]]
deps = ["Base64"]
uuid = "d6f4376e-aef5-505a-96c1-9c027394607a"

[[MathOptInterface]]
deps = ["BenchmarkTools", "CodecBzip2", "CodecZlib", "JSON", "JSONSchema", "LinearAlgebra", "MutableArithmetics", "OrderedCollections", "SparseArrays", "Test", "Unicode"]
git-tree-sha1 = "575644e3c05b258250bb599e57cf73bbf1062901"
uuid = "b8f27783-ece8-5eb3-8dc8-9495eed66fee"
version = "0.9.22"

[[MathProgBase]]
deps = ["LinearAlgebra", "SparseArrays"]
git-tree-sha1 = "9abbe463a1e9fc507f12a69e7f29346c2cdc472c"
uuid = "fdba3010-5040-5b88-9595-932c9decdf73"
version = "0.7.8"

[[MbedTLS]]
deps = ["Dates", "MbedTLS_jll", "Random", "Sockets"]
git-tree-sha1 = "1c38e51c3d08ef2278062ebceade0e46cefc96fe"
uuid = "739be429-bea8-5141-9913-cc70e7f3736d"
version = "1.0.3"

[[MbedTLS_jll]]
deps = ["Artifacts", "Libdl"]
uuid = "c8ffd9c3-330d-5841-b78e-0817d7145fa1"

[[Mmap]]
uuid = "a63ad114-7e13-5084-954f-fe012c677804"

[[MozillaCACerts_jll]]
uuid = "14a3606d-f60d-562e-9121-12d972cd8159"

[[MutableArithmetics]]
deps = ["LinearAlgebra", "SparseArrays", "Test"]
git-tree-sha1 = "3927848ccebcc165952dc0d9ac9aa274a87bfe01"
uuid = "d8a4904e-b15c-11e9-3269-09a3773c0cb0"
version = "0.2.20"

[[NaNMath]]
git-tree-sha1 = "bfe47e760d60b82b66b61d2d44128b62e3a369fb"
uuid = "77ba4419-2d1f-58cd-9bb1-8ffee604a2e3"
version = "0.3.5"

[[NetworkOptions]]
uuid = "ca575930-c2e3-43a9-ace4-1e988b2c1908"

[[OpenBLAS32_jll]]
deps = ["Artifacts", "CompilerSupportLibraries_jll", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "ba4a8f683303c9082e84afba96f25af3c7fb2436"
uuid = "656ef2d0-ae68-5445-9ca0-591084a874a2"
version = "0.3.12+1"

[[OpenSpecFun_jll]]
deps = ["Artifacts", "CompilerSupportLibraries_jll", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "13652491f6856acfd2db29360e1bbcd4565d04f1"
uuid = "efe28fd5-8261-553b-a9e1-b2916fc3738e"
version = "0.5.5+0"

[[OrderedCollections]]
git-tree-sha1 = "85f8e6578bf1f9ee0d11e7bb1b1456435479d47c"
uuid = "bac558e1-5e72-5ebc-8fee-abe8a469f55d"
version = "1.4.1"

[[Parsers]]
deps = ["Dates"]
git-tree-sha1 = "438d35d2d95ae2c5e8780b330592b6de8494e779"
uuid = "69de0a69-1ddd-5017-9359-2bf0b02dc9f0"
version = "2.0.3"

[[Pkg]]
deps = ["Artifacts", "Dates", "Downloads", "LibGit2", "Libdl", "Logging", "Markdown", "Printf", "REPL", "Random", "SHA", "Serialization", "TOML", "Tar", "UUIDs", "p7zip_jll"]
uuid = "44cfe95a-1eb2-52ea-b672-e2afdf69b78f"

[[Preferences]]
deps = ["TOML"]
git-tree-sha1 = "00cfd92944ca9c760982747e9a1d0d5d86ab1e5a"
uuid = "21216c6a-2e73-6563-6e65-726566657250"
version = "1.2.2"

[[Printf]]
deps = ["Unicode"]
uuid = "de0858da-6303-5e67-8744-51eddeeeb8d7"

[[REPL]]
deps = ["InteractiveUtils", "Markdown", "Sockets", "Unicode"]
uuid = "3fa0cd96-eef1-5676-8a61-b3b8758bbffb"

[[Random]]
deps = ["Serialization"]
uuid = "9a3f8284-a2c9-5f02-9a11-845980a1fd5c"

[[SHA]]
uuid = "ea8e919c-243c-51af-8825-aaa63cd721ce"

[[Serialization]]
uuid = "9e88b42a-f829-5b0c-bbe9-9e923198166b"

[[SharedArrays]]
deps = ["Distributed", "Mmap", "Random", "Serialization"]
uuid = "1a1011a3-84de-559e-8e89-a11a2f7dc383"

[[Sockets]]
uuid = "6462fe0b-24de-5631-8697-dd941f90decc"

[[SparseArrays]]
deps = ["LinearAlgebra", "Random"]
uuid = "2f01184e-e22b-5df5-ae63-d93ebab69eaf"

[[SpecialFunctions]]
deps = ["ChainRulesCore", "LogExpFunctions", "OpenSpecFun_jll"]
git-tree-sha1 = "a322a9493e49c5f3a10b50df3aedaf1cdb3244b7"
uuid = "276daf66-3868-5448-9aa4-cd146d93841b"
version = "1.6.1"

[[StaticArrays]]
deps = ["LinearAlgebra", "Random", "Statistics"]
git-tree-sha1 = "3240808c6d463ac46f1c1cd7638375cd22abbccb"
uuid = "90137ffa-7385-5640-81b9-e52037218182"
version = "1.2.12"

[[Statistics]]
deps = ["LinearAlgebra", "SparseArrays"]
uuid = "10745b16-79ce-11e8-11f9-7d13ad32a3b2"

[[TOML]]
deps = ["Dates"]
uuid = "fa267f1f-6049-4f14-aa54-33bafae1ed76"

[[Tar]]
deps = ["ArgTools", "SHA"]
uuid = "a4e569a6-e804-4fa4-b0f3-eef7a1d5b13e"

[[Test]]
deps = ["InteractiveUtils", "Logging", "Random", "Serialization"]
uuid = "8dfed614-e22c-5e08-85e1-65c5234f0b40"

[[TranscodingStreams]]
deps = ["Random", "Test"]
git-tree-sha1 = "216b95ea110b5972db65aa90f88d8d89dcb8851c"
uuid = "3bb67fe8-82b1-5028-8e26-92a6c54297fa"
version = "0.9.6"

[[URIs]]
git-tree-sha1 = "97bbe755a53fe859669cd907f2d96aee8d2c1355"
uuid = "5c2747f8-b7ea-4ff2-ba2e-563bfd36b1d4"
version = "1.3.0"

[[UUIDs]]
deps = ["Random", "SHA"]
uuid = "cf7118a7-6976-5b1a-9a39-7adc72f591a4"

[[Unicode]]
uuid = "4ec0a83e-493e-50e2-b9ac-8f72acf5a8f5"

[[ZipFile]]
deps = ["Libdl", "Printf", "Zlib_jll"]
git-tree-sha1 = "c3a5637e27e914a7a445b8d0ad063d701931e9f7"
uuid = "a5390f91-8eb1-5f08-bee0-b1d1ffed6cea"
version = "0.9.3"

[[Zlib_jll]]
deps = ["Libdl"]
uuid = "83775a58-1f1d-513f-b197-d71354ab007a"

[[nghttp2_jll]]
deps = ["Artifacts", "Libdl"]
uuid = "8e850ede-7688-5339-a07c-302acd2aaf8d"

[[p7zip_jll]]
deps = ["Artifacts", "Libdl"]
uuid = "3f19e933-33d8-53b3-aaab-bd5110c3b7a0"
"""

# ╔═╡ Cell order:
# ╠═457e4d2c-0225-11ec-1b21-7b47b5339342
# ╠═7f3a1eb1-63a7-4062-9dd6-e88e31e961da
# ╠═af9691bd-e434-48e5-bb53-7b63b0d152a9
# ╠═c199a311-3874-4f2c-a6e9-270cbc40cedd
# ╠═8b62d21e-9774-4c5c-9667-c6379e78733c
# ╠═5963c706-4143-443f-aaf0-d61001bfce04
# ╠═2a365ed7-5e15-4b96-851f-2fa556941b51
# ╟─00000000-0000-0000-0000-000000000001
# ╟─00000000-0000-0000-0000-000000000002
