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Yuki Nishimura, Ellen H. Fukuda, Nobuo Yamashita2024 Volume 67 Issue 1 Pages 1-17
Published: January 31, 2024
Released on J-STAGE: February 01, 2024
JOURNAL FREE ACCESSAccelerated proximal gradient methods, which are also called fast iterative shrinkage-thresholding algorithms (FISTA) are known to be efficient for many applications. Recently, Tanabe et al. proposed an extension of FISTA for multiobjective optimization problems. However, similarly to the single-objective minimization case, the objective functions values may increase in some iterations, and inexact computations of subproblems can also lead to divergence. Motivated by this, here we propose a variant of the FISTA for multiobjective optimization, that imposes some monotonicity of the objective functions values. In the single-objective case, we retrieve the so-called MFISTA, proposed by Beck and Teboulle. We also prove that our method has global convergence with rate O(1/k2), where k is the number of iterations, and show some numerical advantages in requiring monotonicity.
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Koji Kusuda2024 Volume 67 Issue 1 Pages 18-36
Published: January 31, 2024
Released on J-STAGE: February 01, 2024
JOURNAL FREE ACCESSThis study shows that Arrow–Debreu equilibria in a continuous-time market economy with an infinite-dimensional martingale generator can be implemented in “approximately complete security markets,” in which every bond of any maturity is traded and any contingent claim is approximately replicated with any given precision. I introduce “approximate security market equilibrium” as a generalized concept of security market equilibrium. I demonstrate that an Arrow–Debreu equilibrium in the economy can be identified with an approximate security market equilibrium in the approximately complete markets.
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