{"id":2467,"date":"2023-06-27T15:14:06","date_gmt":"2023-06-27T15:14:06","guid":{"rendered":"https:\/\/nag.com\/?page_id=2467"},"modified":"2023-06-27T15:14:51","modified_gmt":"2023-06-27T15:14:51","slug":"active-set-method-for-nonlinear-optimization","status":"publish","type":"page","link":"https:\/\/nag.com\/active-set-method-for-nonlinear-optimization\/","title":{"rendered":"Active-set Method for Nonlinear Optimization"},"content":{"rendered":"\n
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Active-set Method for Nonlinear Optimization<\/h1>\n \n

n<\/i><\/span>AG Library mini-article<\/p>\n<\/div>\n\n \n <\/div>\n <\/div>\n <\/div>\n <\/div>\n <\/div>\n<\/div>\n\n\n\n

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One of the key algorithms to address general constrained nonlinear optimization problems is an active-set sequential quadratic programming (SQP) method. It is a workhorse for many commercial and open-source solvers. The n<\/i><\/span>AG\u00ae Library offers a state-of-the-art version within the\u00a0Optimization Modelling Suite<\/a>. It complements n<\/i><\/span>AG’s\u00a0interior point method (IPM)<\/a>\u00a0and other specialized methods for nonlinear optimization such as\u00a0Derivative Free Optimization (DFO)<\/a>\u00a0or\u00a0first order method<\/a>.<\/p>\n

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Applications<\/h3>\n
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NLP is commonplace across many industries and is used within real-world applications, such as optimal control, for example, trajectory optimization, robotics and other optimization of processes described by differential equations, engineering, finance or manufacturing amongst many myriads of examples.<\/p>\n<\/div>\n

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How the Active-Set Method Works<\/h3>\n
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Our active-set nonlinear solver solves at each iteration a quadratic approximation of the original problem and it tries to estimate which constraints need to be kept (are active) and which can be ignored. A practical consequence is that the algorithm partly \u201cwalks along the boundary\u201d of the feasible region given by the constraints. The iterates are thus early on feasible with regard to all linear constraints (and a local linearization of the nonlinear constraints) which is preserved through the iterations. The complementarity is satisfied by default and once the active set is determined correctly and optimality is within the tolerance, the solver finishes. The number of iterations might be high, but each is relatively cheap.<\/p>\n

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Important Update of the Sparse SQP Solver at Mark 28.4<\/h3>\n
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Performance and stability improvements<\/strong>\u00a0\u2013 Benchmark studies on 826 NLP (CUTEst) problems show that the new\u00a0handle_solve_ssqp<\/a>\u00a0(e04sr<\/a>) is faster than the solver it replaces\u00a0nlp2_sparse_solve<\/a>\u00a0(e04vh<\/a>) in at least 10% of problems. It also revealed that e04sr is more robust that e04vh, solving 6.7% more problems. Specifically, it reveals that it is 25% faster in 13% of the problems and twice as fast on 5.7% of the problems. For the hardest 10% of the problems, e04sr is 1.25 times faster in 33% of those.<\/p>\n<\/div>\n

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New intuitive interface<\/strong>\u00a0\u2013 the n<\/i><\/span>AG\u00ae\u00a0Optimization Modelling Suite<\/a>\u00a0provides an easy to use interface for the solver including an extended modelling feature with a rich API to define problems and allowing for easy switching between different algorithms as and when required.<\/p>\n

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Try The n<\/i><\/span>AG Library Now<\/h1>\n \n
<\/div>\n\n \n Trial Now <\/i><\/a> <\/div>\n <\/div>\n <\/div>\n <\/div>\n <\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"","protected":false},"author":3,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"content-type":"","footnotes":""},"class_list":["post-2467","page","type-page","status-publish","hentry"],"yoast_head":"\nActive-set Method for Nonlinear Optimization - nAG<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/nag.com\/active-set-method-for-nonlinear-optimization\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Active-set Method for Nonlinear Optimization - nAG\" \/>\n<meta property=\"og:url\" content=\"https:\/\/nag.com\/active-set-method-for-nonlinear-optimization\/\" \/>\n<meta property=\"og:site_name\" content=\"nAG\" \/>\n<meta property=\"article:modified_time\" content=\"2023-06-27T15:14:51+00:00\" \/>\n<meta property=\"og:image\" content=\"https:\/\/nag.com\/wp-content\/uploads\/2024\/02\/NAG-Logo-White-On-Blue.jpg\" \/>\n\t<meta property=\"og:image:width\" content=\"12770\" \/>\n\t<meta property=\"og:image:height\" content=\"4353\" \/>\n\t<meta property=\"og:image:type\" content=\"image\/jpeg\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:site\" content=\"@NAGTalk\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\/\/schema.org\",\"@graph\":[{\"@type\":\"WebPage\",\"@id\":\"https:\/\/nag.com\/active-set-method-for-nonlinear-optimization\/\",\"url\":\"https:\/\/nag.com\/active-set-method-for-nonlinear-optimization\/\",\"name\":\"Active-set Method for Nonlinear Optimization - 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