이화여자대학교

김선영(金善英) 교수

수학과

김선영 프로필 사진 
김선영 교수는 수학전공 소속 교수로 응용수학, 수치해석 분야의 강의와 연구를 진행하고 있다. 
미국 뉴욕주 뉴욕주립대학(스토니부룩)에서 응용수학으로 박사학위를 받았으며, 수학의 응용문제에 대한 이론과 계산의 연구를 수행하고 있다. 현재 연구의 상세분야는 최적화 혹은 수리계획법이다. 최근 이 분야에서 주목받는 주제인 다항식최적화문제, 유클리디언거리행렬문제, 완전한 양의 계획법 등을 대상으로 연구하고 있다. 특히, 성김성을 이용하여 해법의 효율성을 높이는 알고리즘개발이 주목을 받고 있다.      
강의는 수치해석, 응용수학, 최적화, 선형대수 등을 담당하고 있다.
  • 종합과학관 A동 A511호
  • 02-3277-2379
  • 면담 가능시간
    • 화 2:00-4:00
연구실적
  • [학술지논문] An Exceptionally Difficult Binary Quadratic Optimization Problem with Symmetry: a Challenge for The Largest Unsolved QAP Instance Tai256c OPTIMIZATION LETTERS, 2025, v.. no.. , .-.
    SCIE
  • [학술지논문] Equivalent Sufficient Conditions for Global Optimality of Quadratically Constrained Quadratic Program MATHEMATICAL METHODS OF OPERATIONS RESEARCH, 2025, v... no... , ..-..
    SCIE
  • [학술지논문] FURTHER DEVELOPMENT IN CONVEX CONIC REFORMULATION OF GEOMETRIC NONCONVEX CONIC OPTIMIZATION PROBLEMS SIAM JOURNAL ON OPTIMIZATION, 2024, v.34 no.4 , 3194-3211
    SCIE
  • [학술지논문] T-semidefinite programming relaxation with third-order tensors for constrained polynomial optimization COMPUTATIONAL OPTIMIZATION AND APPLICATIONS, 2024, v.89 no.1 , 183-218
    SCIE
  • [학술지논문] Exact SDP relaxations for quadratic programs with bipartite graph structures JOURNAL OF GLOBAL OPTIMIZATION, 2023, v.86 no.3 , 671-691
    SCIE
  • [학술지논문] Strong duality of a conic optimization problem with a single hyperplane and two cone constraints OPTIMIZATION, 2023, v.2023 no.0 , 2251987-2251987
    SCIE
  • [학술지논문] Doubly nonnegative relaxations for quadratic and polynomial optimization problems with binary and box constraints MATHEMATICAL PROGRAMMING, 2022, v.193 no.2 , 761-787
    SCI
  • [학술지논문] Exact SDP relaxations of quadratically constrained quadratic programs with forest structures JOURNAL OF GLOBAL OPTIMIZATION, 2022, v.82 no.2 , 243-262
    SCI
  • [학술지논문] A Newton-bracketing method for a simple conic optimization problem OPTIMIZATION METHODS & SOFTWARE, 2021, v.36 no.2-3 , 371-388
    SCIE
  • [학술지논문] A GEOMETRICAL ANALYSIS ON CONVEX CONIC REFORMULATIONS OF QUADRATIC AND POLYNOMIAL OPTIMIZATION PROBLEMS SIAM JOURNAL ON OPTIMIZATION, 2020, v.30 no.2 , 1251-1273
    SCI
  • [학술지논문] A dual spectral projected gradient method for log-determinant semidefinite problems COMPUTATIONAL OPTIMIZATION AND APPLICATIONS, 2020, v.76 no.1 , 33-68
    SCI
  • [학술지논문] Doubly nonnegative relaxations are equivalent to completely positive reformulations of quadratic optimization problems with block-clique graph structures JOURNAL OF GLOBAL OPTIMIZATION, 2020, v.77 no.3 , 513-541
    SCI
  • [학술지논문] Algorithm 996: BBCPOP: A Sparse Doubly Nonnegative Relaxation of Polynomial Optimization Problems With Binary, Box, and Complementarity Constraints ACM TRANSACTIONS ON MATHEMATICAL SOFTWARE, 2019, v.45 no.3 , 34-34
    SCI
  • [학술지논문] LAGRANGIAN-CONIC RELAXATIONS, PART II: APPLICATIONS TO POLYNOMIAL OPTIMIZATION PROBLEMS PACIFIC JOURNAL OF OPTIMIZATION, 2019, v.15 no.3 , 415-439
    SCIE
  • [학술지논문] On the conditions for the finite termination of ADMM and its applications to SOS polynomials feasibility problems COMPUTATIONAL OPTIMIZATION AND APPLICATIONS, 2019, v.74 no.2 , 317-344
    SCI
  • [학술지논문] Solving pooling problems with time discretization by LP and SOCP relaxations and rescheduling methods JOURNAL OF GLOBAL OPTIMIZATION, 2019, v.75 no.3 , 631-654
    SCI
  • [학술지논문] Equivalences and differences in conic relaxations of combinatorial quadratic optimization problems JOURNAL OF GLOBAL OPTIMIZATION, 2018, v.72 no.4 , 619-653
    SCI
  • [학술지논문] LAGRANGIAN-CONIC RELAXATIONS, PART I: A UNIFIED FRAMEWORK AND ITS APPLICATIONS TO QUADRATIC OPTIMIZATION PROBLEMS PACIFIC JOURNAL OF OPTIMIZATION, 2018, v.14 no.1 , 161-192
    SCIE
  • [학술지논문] A robust Lagrangian-DNN method for a class of quadratic optimization problems COMPUTATIONAL OPTIMIZATION AND APPLICATIONS, 2017, v.66 no.3 , 453-479
    SCI
  • [학술지논문] Binary quadratic optimization problems that are difficult to solve by conic relaxations DISCRETE OPTIMIZATION, 2017, v.24 no.Special SI , 170-183
    SCIE
  • [학술지논문] EXACT SEMIDEFINITE PROGRAMMING RELAXATIONS WITH TRUNCATED MOMENT MATRIX FOR BINARY POLYNOMIAL OPTIMIZATION PROBLEMS SIAM JOURNAL ON OPTIMIZATION, 2017, v.27 no.1 , 565-582
    SCI
  • [학술지논문] A Lagrangian-DNN relaxation: a fast method for computing tight lower bounds for a class of quadratic optimization problems MATHEMATICAL PROGRAMMING, 2016, v.156 no.1-2 , 161-187
    SCI
  • [학술지논문] Extension of Completely Positive Cone Relaxation to Moment Cone Relaxation for Polynomial Optimization JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS, 2016, v.168 no.3 , 884-900
    SCI
  • [학술지논문] Semidefinite programming relaxation methods for global optimization problems with sparse polynomials and unbounded semialgebraic feasible sets JOURNAL OF GLOBAL OPTIMIZATION, 2016, v.65 no.2 , 175-190
    SCI
  • [학술지논문] SIMPLIFIED COPOSITIVE AND LAGRANGIAN RELAXATIONS FOR LINEARLY CONSTRAINED QUADRATIC OPTIMIZATION PROBLEMS IN CONTINUOUS AND BINARY VARIABLES PACIFIC JOURNAL OF OPTIMIZATION, 2014, v.10 no.3 , 437-451
    SCIE
  • [학술지논문] A CONTINUATION METHOD FOR LARGE-SIZED SENSOR NETWORK LOCALIZATION PROBLEMS PACIFIC JOURNAL OF OPTIMIZATION, 2013, v.9 no.0 , 117-136
    SCI
  • [학술지논문] A QUADRATICALLY CONSTRAINED QUADRATIC OPTIMIZATION MODEL FOR COMPLETELY POSITIVE CONE PROGRAMMING SIAM JOURNAL ON OPTIMIZATION, 2013, v.23 no.4 , 2320-2340
    SCI
  • [학술지논문] Algorithm 920: SFSDP: A Sparse Version of Full Semidefinite Programming Relaxation for Sensor Network Localization Problems ACM TRANSACTIONS ON MATHEMATICAL SOFTWARE, 2012, v.38 no.4 , 1-1
    SCI
  • [학술지논문] EXPLOITING SPARSITY IN SDP RELAXATION FOR SENSOR NETWORK LOCALIZATION SIAM JOURNAL ON OPTIMIZATION, 2009, v.20 , 192-215
    SCI
  • [학술지논문] Recognizing underlying sparsity in optimization MATHEMATICAL PROGRAMMING, 2009, v.119 , 273-303
    SCI
  • [학술지논문] SPARSE SECOND ORDER CONE PROGRAMMING FORMULATIONS FOR CONVEX OPTIMIZATION PROBLEMS JOURNAL OF THE OPERATIONS RESEARCH SOCIETY OF JAPAN, 2008, v.51 no.3 , 241-264
    SCIE
  • [학술지논문] SparsePOP - A sparse semidefinite programming relaxation of polynomial optimization problems ACM TRANSACTIONS ON MATHEMATICAL SOFTWARE, 2008, v.35 no.2 , 121-134
    SCI
  • [학술발표] Convex conic reformulation of geometric nonconvex conic optimization problems and exact solutions of QCQPs by semidefinite relaxations ISMP (Internatioanl Symposium on Mathematical Programming) 2024, 캐나다, Montreal, 2024-07-26 ISMP Proceeding, 2024, 145-145
  • [학술발표] High-rank Solution of Sum-of-Squares Relaxations for Exact Matrix Completion ISMP(International Symposium on Mathematical Programming) 2024, 캐나다, Montreal, 2024-07-26 ISMP Proceeding, 2024, 145-145
  • [학술발표] Solving Large-Scale Quadratic Assignment Problems by a Parallelized Lagrangian-DNN-Based Branch-and-Bound ISMP(International Symposium on Mathematical Programming) 2024, 캐나다, Montreal, 2024-07-24 ISMP Proceeding, 2024, 330-330
  • [학술발표] Convex Conic Reformulations of Geometric Nonconvex Conic Optimization Problems for a Class of Quadratic Optimization Problems SIAM Optimizaiton Meeting 2023, 미국, Seattle, 2023-06-01 SIAM Society Proceeding, 2023, 95-95
  • [학술발표] Equivalent Sufficient Conditions for Exact SDP Relaxation and the Saddle Point of Lagrangian Function of QCQP ICIAM 2023, 일본, Tokyo, 2023-08-23 Proceedings of ICIAM 2023, 2023
  • [학술발표] Tight Semidefinite Relaxations for Sign-Indefinite Qcqps with Bipartite Structures SIAM Optimizaiton Meeting 2023, 미국, Seattle, 2023-06-01 SIAM Society Proceeding, 2023, 94-94
  • [학술발표] Tightness conditions of SDP relaxation for QCQPs with bipartite graph structure ICIAM 2023, 일본, Tokyo, 2023-08-23 Proceedings of ICIAM 2023, 2023, .-.
  • [학술발표] Exact conic relaxations for quadratic optimization problems International Workshop on Continuous Optimization, 일본, Tokyo, 2022-12-03 International Workshop on Continuous Optimization 2022, 2022, 10-10
  • [학술발표] A Newton-Bracketing Method for Quadratic and Polynomial Optimization Problems SIAM Optimization 2021, 미국, 2021-07-22 SIAM Proceeding, 2021, 287-287
  • [학술발표] Doubly nonnegative Relaxations and Completely Positive Reformulations of Quadratic Optimization Problems with Block-Clique Structures The 2nd Greater Bay Area Worship on Computational Optimization, 홍콩, Hong Kong, 2021-12-11 Greater Bay Area Worship on Computational Optimization, 2021
  • [학술발표] Efficient SOCP Relaxations for Pooling Problems SIAM Optimization 2021, 미국, 2021-07-23 SIAM proceeding, 2021, 309-309
  • [학술발표] Exact semidefinite relaxations for QCQPs with forest- structured matrices and its applications IFORS 2021 , 대한민국, online, 2021-08-24 IFORS 2021 , 2021, 15-15
  • [학술발표] Exactness Conditions for Semidefinite Relaxation of Nonconvex QCQPS with Forest Structures SIAM Optimization 2021, 미국, 2021-07-23 SIAM Opt proceeding, 2021, 309-309
  • [학술발표] A dual spectral projected gradient method for log-determinant semidefinite problems ICCOPT 2019, 독일, 베를린, 2019-08-06 ICCOPT 2019, 2019
  • [학술발표] Doubly nonnegative programs equivalent to completely positive reformulations of quadratic optimization problems with block clique structures ICCOPT 2019, 독일, 베를린, 2019-08-06 ICCOPT 2019, 2019
  • [학술발표] BBCPOP: a Matlab package for sparse DNN relaxations of polynomial optimization problems with binary, box and complementarity conditions International Symposium on Mathematical Programming (ISMP2018), 프랑스, 보르드, 2018-07-03 Proceedings, 2018
  • [학술발표] Solving a convergent hierarchy of DNN relaxations of polynomial optimization problems with the Newton bracketing method ICPTO 2018 (International conference on polynomial and tensor optimization), 중국, XiangTan, 2018-12-20 Proceeding of ICPTO2018, 2018, 12-13
  • [학술발표] A robust Lagrangian-DNN method for a class of quadratic optimization problems ICCOPT 2016, 일본, 2016-08-10 Proceeding of ICCOPT 2016 , 2016
  • [학술발표] SDP and DNN relaxations of discrete polynomial optimization problems ICCOPT 2016, 일본, Tokyo, 2016-08-10 ICCOPT 2016, 2016
  • [학술발표] A numerical study on the sum-of-squares relaxation for a Lagrangian relaxation of quadratic optimization problems with binary variables ISMP 2015 (International Symposium on Mathematical Programming), 미국, Pittsburg, 2015-07-16 ISMP 2015, 2015
  • [학술발표] Lagrangian Doubly Nonnegative Relaxations of Polynomial Optimization Problems SIAM Applied Algebraic Geometry 2015, 대한민국, 대전, 2015-08-07 SIAM Applied Algebraic Geometry 2015, 2015
  • [학술발표] A quadratic optimization model for completely positive programming and its application to 0-1 mixed integer linearly constrained quadratic optimization problems ICCOPT 2013, 포르투갈, lisbon, 2013-08-01 Proceeding of ICCOPT 2013, 2013
  • [학술발표] Extension of completely positive cone relaxation to polynomial optimization ICCOPT 2013 (International Conference on Continuous Optimization), 포르투갈, 리스본, 2013-08-01 Proceeding, 2013
  • [학술발표] A Successive SDP Relaxation Method for Distance Geometry Problems ISMP 2012 (International Symposium on Mathematical Programming, 독일, Berlin, 2012-08-20 ISMP, 2012
  • [학술발표] Exploiting sparsity in SDP relaxation for sensor network localization International Sym. on Math. Programming (ISMP) 2009, 미국, Chicago, 2009-08-27 ISMP 2009, 2009, 99-99
  • [학술발표] Polynomial optimization approach for sensor network localization problems SJOM 2008, 대만, Tiwan, 2008-08-30 SJOM2008, 2008
  • [학술발표] Semidefinite programmging approach for polynomial least squares problems SIAM Optimization 2008, 미국, Boston, 2008-05-11 SIAM Optimization Meeting 2008, 2008
  • [학술발표] Solving polynomial least squares problems via semidefinite programming relaxation RIMS Workshop on Optimization, Kyoto University, 일본, kyoto, 2007-07-19
  • [학술발표] SparsePOP: a Sparse Semidefinite Programming Relaxation of Polynomial Optimization Problems Optimization and control (IMA), 미국, Minnesota, 2007-01-15
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강의

  • 2024-2학기

    • 선형대수학Ⅰ

      • 학수번호 20441분반 01
      • 2학년 ( 3학점 , 4.5시간) 월 5~5 (포362) , 수 4~4 (포362)
      • 재학생(편입생, 복학생, 고학번 미수강자 등), 호크마교양대학1, 선형대수학 I (01~03분반) 연습시간은 통합운영
        • 첨부파일

    • 수치미분방정식

      • 학수번호 34223분반 01
      • 3학년 ( 3학점 , 3시간) 월 6~6 (포360) , 수 5~5 (포360)
        • 첨부파일

  • 2024-1학기

    • 미분적분학Ⅰ 강의 계획서 상세보기

      • 학수번호 20407분반 01
      • 1학년 ( 3학점 , 3시간) 월 3~3 (포452) , 수 2~2 (포452)
      • 연습시간(01~06분반 통합 온라인 운영)
        • 첨부파일

    • 선형대수학Ⅰ 강의 계획서 상세보기

      • 학수번호 20441분반 03
      • 2학년 ( 3학점 , 4.5시간) 월 5~5 (포452) , 수 4~4 (포452)
      • 자연대 및 기타전공(수학과 수강 금지)
        • 첨부파일

  • 2023-2학기

  • 2023-1학기

  • 2022-1학기

    • 수치해석학

      • 학수번호 20445분반 01
      • 3학년 ( 3학점 , 3시간) 화 3~3 (포361) , 목 2~2 (포361)
        • 첨부파일

    • 수치선형대수학

      • 학수번호 G10517분반 01
      • 학년 ( 3학점 , 3시간) 화 4~4 , 목 3~3
        • 첨부파일
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학력

Stony Brook University Ph.D.(응용수학)