Convexifiability of continuous and discrete nonnegative quadratic programs for gap-free duality |
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| Institution: | 1. Applied Analysis Research Group, Faculty of Mathematics and Statistics, Ton Duc Thang University, Ho Chi Minh City, Vietnam;2. Department of Applied Mathematics, University of New South Wales, Sydney 2052, Australia;1. Department of Logistics Management, School of Economics and Management, Beijing Jiaotong University, Beijing 100044, China;2. Department of Logistics and Maritime Studies, The Hong Kong Polytechnic University, Hung Hom, Kowloon, Hong Kong Special Administrative Region;1. Department of Mathematics, Technische Universität Kaiserslautern, Germany;2. School of Mathematics and Natural Sciences, University of Wuppertal, Germany;3. Department of Mathematical Sciences, Clemson University, SC, USA;1. School of Economic Mathematics and Collaborative Innovation Center of Financial Security, Southwestern University of Finance and Economics, Chengdu 611130, China;2. School of Economic Mathematics, Southwestern University of Finance and Economics, Chengdu 611130, China;3. Department of Mathematics, Imperial College, London SW7 2BZ, UK;1. Jiangsu Key Laboratory for NSLSCS, School of Mathematical Sciences, Nanjing Normal University, Nanjing 210023, PR China;2. School of Mathematical Sciences, Nanjing Normal University, Nanjing 210023, PR China;3. School of Mathematics and Systems Science, Beijing Advanced Innovation Center for Big Data and Brain Computing (BDBC), Beihang University, Beijing 100191, PR China |
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| Abstract: | In this paper we show that a convexifiability property of nonconvex quadratic programs with nonnegative variables and quadratic constraints guarantees zero duality gap between the quadratic programs and their semi-Lagrangian duals. More importantly, we establish that this convexifiability is hidden in classes of nonnegative homogeneous quadratic programs and discrete quadratic programs, such as mixed integer quadratic programs, revealing zero duality gaps. As an application, we prove that robust counterparts of uncertain mixed integer quadratic programs with objective data uncertainty enjoy zero duality gaps under suitable conditions. Various sufficient conditions for convexifiability are also given. |
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